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T 



PARADISE OF CHILDHOOD 



A MANUAL FOR SELF-INSTRUCTION IN FRIEDRICH FROEBEL'S 
EDUCATIONAL PRINCU'LES, 



AXD A ntACTICAL 



Glide to Kinder-Gartners. 



EDWARD WIEBE. 



WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS. 



c/ 

MILTON BRADLEY & COMPANY, 

SPRINGFIKLD, MASS. 



Lbins 



Entered according to Act of Congress, in the year 1869, by 
MILTON BRADLEY & COMPANY, 
the Clerk's Office of the District Court of the District of Massachusetts. 



SAMUEL BOWLES AND COMPANY, 
PRINTERS, ELECTKOTYPERS, AND BINDERS, 

SPRINGFIELD, MASS. 



ERRATA. 

PI,ATE XI. Fir.. i6. — Upper row to consist of four whole cubes. 

Fig 19. — In the second row the 2nd and 4th square, on either side should be open, so as to repre- 
sent windows. 
Fig. 21.— The remaining whole cube is to be placed upon the center in the first row. 
PLATE XIII, Fig. 30. — Eight quarter blocks should be connected here with the four outermost whole blocks as 

in figures 28 and 29. 
PLATE XIV, Fig 51. — Six quarter cubes form star in center as in figure 52. 
PLATE XVII, Fig. 3. — The blocks forming back wall should stand on those forming foundation. 
PLATE XIX, Fig. 3. — The four corner pieces are to be like those in figure 2 
PLATE XX, Fig. 21 in the perspective should extend in front over six squares only. 

Fig. 23. — There should be an open space in the center of two squares, one above the other. 
PLATE XXII, Fig. 117. — Left upper part should be shaded like the right lower one. 
PLATE XLVI, Fig. 5. — The two halves of the figure ought to connect as in figure 4. 



INTRODUCTION. 



Until a recent period, but little interest has been 
felt by people in this country, with regard to the 
Kinder-Garten method of instruction, for the simple 
reason that a correct knowledge of the system has 
never been fully promulgated here. However the lec- 
tures of Miss E. P. Peabody of Cambridge, Mass., 
have awakened some degree of enthusiasm upon the 
subject in different localities, and the establishment 
of a few Kinder-Garten schools has served to call forth 
a more general inquiry concerning its merits. 

We claim that every one who believes in rational 
education, will become deeply interested in the pecu- 
liar features of the work, after having become ac- 
quainted with Froebel's principles and plan ; and 
that all that is needed to enlist the popular sentiment 
in its favor is the establishment of institutions of this 
kind, in this country, upon the right basis. 

With such an object in view, we propose to present 
an outline of the Kinder-Garten plan as developed by 
its originator in Germany, and to a considerable ex- 
tent by his followers in France and England. 

But as Froebel's is a system which must be carried 
out faithfully in all its important features, to insure 
success, we must adopt his plan as a whole and carry 
it out with such modifications of secondary minutia; 
only, as the individual case may acquire without vio- 
lating its fundamental principles. If this cmnot be 
accomplished, it were better not to attempt the task 
at all. 

The present work is entitled a Manual for Self- 
Instruction and a Practical Guide for Kinder-Gartners. 
Those who design to use it for either of these pur- 
poses, must not expect to find in it all that they ought to 



know in order to instruct the young successfully ac- 
cording to Froebel's principles. No book can ever 
be written which is able to make a perfect Kinder- 
Gartner ; this requires the training of an able teacher 
actively engaged in the work at the moment 
" Kinder-Garten Culture," says Miss Peabody, in the 
preface to her "Moral Culture of Infancy," "is the 
adult mind entering into the child's world and ap- 
preciating nature's intention as displayed in every 
impulse of spontaneous life, so directing it that the 
joy of success may be ensured at every step, and 
artistic things be actually produced, which gives the 
selfreliance and conscious intelligence that ought to 
discriminate human power from blind force." 

With this thought constantly present in his mind, 
the reader will find, in this book, all that is indispens- 
ably necessary for him to know, from the first estab- 
lishment of the Kinder-Garten through all its various 
degrees of development, including the use of the mate- 
rials and the engagement in such occupations as are 
peculiar to the system. There is much more, how- 
ever, that can be learned only by individual obser- 
vation. The fact, that here and there, persons, pre- 
suming upon the slight knowledge which they may 
have gained of Froebel and his educational principles, 
from books, have established schools called Kinder- 
Gartens, which in reality had nothing in common with 
the legitimate Kinder-Garten but the name, has caused 
distrust and even opposition, in many minds towards 
everything that pertains to this method of instruc- 
tion. In discriminating between the spurious and the 
real, as is the design of this work, the author would 
mention with special commendation, the Educational 



IV 



INTRODUCTION. 



Institute conducted by Mrs. and Miss Kriege in 
Boston. It connects with the Kinder-Garten proper, 
a Training School for ladies, and any one who wishes 
to be instructed in the correct method, will there be 
able to acquire the desired knowledge. 

Besides the Institute just mentioned, there is one 
in Springfield, Mass., under the supervision of the 
writer, designed not only for the instruction of classes 
of children in accordance with these principles, but 
also for imparting information to those who are de- 
sirous to become Kinder-Gartners. From this source, 
the method has already been acquired in several in- 
stances, and as one result, it has been introduced into 
two of the schools connected with the State Institu- 
tion at Monson, Mass. 

The writer was in early life acquainted with Froebel ; 
and his subsequent experience as a teacher has only 
served to confirm the favorable opinion of the system, 
which he then derived from a personal knowledge of 



its inventor. A desire to promote the interests of true 
education, has led him to undertake this work of inter- 
pretation and explanation. 

Withput claiming for it perfection, he believes that, 
as a guide, it will stand favorably in comparison with 
any publication upon the subject in the English or the 
French language. 

The German of Marenholtz, Goldammer, Morgen- 
stern and Froebel have been made use of in its prep- 
aration, and though new features have, in rare cases 
only, been added to the original plan, several changes 
have been made in minor details, so as to adapt this 
mode of instruction more readily to the American 
mind. This has been done, however, without omit- 
ting aught of that German thoroughness, which char- 
acterizes so strongly every feature of Froebel's system. 

The plates accompanying this work are reprints 
from " Goldammer's Kinder-Garten," a book recently 
published in Germany. 



The Paradise of Childhood : 
A GUIDE TO KINDER-GARTNERS. 



ESTABLISHMENT OF A KINDER-GARTEN. 



The requisites for the establishment of a 
" Kinder-Garten " are the following : 

1. A house, containing at least one large 
room, spacious enough to allow the children, 
not only to engage in all their occupations, 
both sitting and standing, but also to practice 
their movement plays, which, during inclem- 
ent seasons, must be done in-dcors. 

2. Adjoining the large room, one or two- 
smaller rooms for sundry purposes. 

3. A number of tables, according to the 
size of the school, each table affording a 
smooth surface ten feet long and four feet 
wide, resting on movable frames from eighteen 
to twenty-four inches high. The table should 
be divided into ten equal squares, to accom- 
modate as many pupils ; and each square 
subdivided into smaller squares of one inch, 
to guide the children in many of their occu- 
pations. On either side of the tables should 
be settees with folding seats, or small chairs 
ten to fifteen inches high. The tables and 
settees should not be fastened to the floor, as 
they will need to be removed at times to 
make room for occupations in which they are 
not used. 

4. A piano-forte for gjmnastic and musical 
exercises — the latter being an important feat- 
ure of the plan, since all the occupations are 
interspersed with, and many of them accom- 
panied by, singing. 

5. Various closets for keeping the apparatus 
and work of the children — a wardrobe, wash- 
stand, chairs, teacher's table, &c. 



The house should be pleasantly located, 
removed from the bustle of a thoroughfare, 
and its rooms arranged with strict regard to 
hygienic principles. A garden should sur- 
round or, at least, adjoin the building, for 
frequent out door exercises, and for gardening 
purposes. A .=niall plot is assigned to each 
child, in which he sows the seeds and culti- 
vates the plants, receiving, in due time, the 
flowers or fruits, as the result of his industry 
and care. 

When a Training School is connected with 
the'Kinder-Garten, the children of the "Gar-^ 
ten " are divided into groups of five or ten — 
each group being assisted in its occupations 
by one of the lady pupils attending the Train- 
ing School. 

Should there be a greater number of such 
assistants than can be conveniently occupied 
in the Kinder Garten, they may take turns 
with each other. In a Training School of 
this kind, under the charge of a competent 
director, ladies are enabled to acquire a thor- 
ough and practical knowledge of the system. 
They should bind themselves, however, to 
remain connected with the institution a speci- 
fied time, and to follow out the details of the 
method patiently, if they aim to fit themselves 
to conduct a Kinder-Garten with success. 

In any establishment of more than twenty 
children, a nurse should be in constant at- 
tendance. It should be her duty also to 
preserve order and cleanliness in the rooms, 
and to act as janitrix to the institution. 



MEANS AND WAYS OF OCCUPATION 

IN THE KINDER-GARTEN. 



Before entering into a description of the 
various means of occupation in tlie Kinder- 
Garten, it will be proper to state that Fried- 
rich Froebel, the inventor of this system of 
education, calls all ocaipations in the Kinder- 
Garten '■^ plays" and the materials for occupa- 
tion '■^ gifts." In these systematically-arranged 
plays, Froebel starts from the fundamental 
idea that all education should begin with a 
development of the desire for activity innate 
in the child; and he has been, as is universally 
acknowledged, eminently successful in this 
part of his important work. Each step in 
the course of training is a logical sequence 
of the preceding one ; and the various means 
of occupation are developed, one from another, 
in a perfectly natural order, beginning with the 
simplest and concluding with the most difficult 
features in all the varieties of occupation. To- 
gether, they satisfy all the demands of the child's 
nature in respect both to mental and physical 
culture, and lay the surest foundation for all 
subsequent education in school and in life. 

Th& time of occupation in the Kinder-Garten 
is three or four hours on each week day, usually 
from 9 to 1 2 or I o'clock ; and the time allot- 
ted to each separate occupation, including the 
changes from one to another, is from twenty to 
thirty minutes. Movement plays, so-called, in 
which the children imitate the flying of birds, 
swimming of fish, the motions of sowing, mow- 
wing, threshing, &c., in connection with light 
gymnastics and vocal exercises, alternate with 
the plays performed in a sitting posture. All 
occupations that can be engaged in out of 
doors, are carried on in the garden whenever 
the season and weather permit. 



For the reason that the various occupations, 
as previously stated, are so intimately con- 
nected, growing, as it were, out of each other, 
they are introduced very gradually, so as to 
afford each child ample time to become suffi- 
ciently prepared for the next step, without 
interfering, however, with the rapid progress 
of such as are of a more advanced age, or 
endowed with stronger or better developed 
faculties. 

The following is a list of the gifts or ma- 
"terial and means of occupation in the Kinder- 
Garten, each of which will be specified and 
described separately hereafter. 

There are altogether twenty gifts, according 
to Froebel's general definition of the term, al- 
though the first six only are usually designated 
by this name. We choose to follow the classi- 
fication and nomenclature of the great inventor 
of the system. 

LIST OF FROEBEL'S GIFTS. 

1. Six rubber balls, covered with a net-work 
of twine or worsted of various colors. 

2 . Sphere, cube, and cylinder, made of wood. 

3. Large cube, consisting of eight small 
cubes. 

4. Large cube, consisting of eight oblong 
parts. 

5. Large cube, consisting of whole, half, 
and quarter tubes. 

6. Large cube, consisting of doubly divided 
oblongs. 

[The third, fourth, fifth and sixth gifts serve 
for building purposes.] 

7. Square and triangular tablets for laying 
of figures. 



GUIDE TO KINDER- GARTNERS. 



8. Staffs for laying of figures. 

9. Whole and half rings for laying of 
figures. 

10. Material for drawing. 

11. Material for perforating. 

12. Material for embroidering. 

13. Material for cutting of paper and com- 
bining pieces. 



14. Material for braiding. 

15. Slats for interlacing. 

16. The slat with many links. 

17. Material for intertwining. 

18. Material for paper folding. 

19. Material for peas-work. 

20. Material for modeling. 



THE FIRST GIFT. 



The First Gift, which consists of sLx rubber 
balls, over-wrought with worsted, for the pur- 
pose of representing the three fundamental 
and three mLxed colors, is introduced in this 
manner: 

The children are made to stand in one or 
two rows, with heads erect, and feet upon a 
given line, or spots marked on tlie floor. 
The teacher then gives directions like the 
following : 

" Lift up your right hands as high as you 
can raise them." 

" Take them down." 

" Lift up your left hands." " Down." 

" Lift up both your hands." " Down." 

" Stretch forward your right hands, that I 
may give each of you something tliat I have 
in my box." 

The teacher then places a ball in the hand 
of each child, and asks — 

" Who can tell me the -name of what you 
have received ? " Questions may follow about 
the color, material, shape, and other qualities 
of the ball, which will call forth the replies, 
blue, yellow, rubber, round, light, soft, &c. 

The children are then required to repeat 
sentences pronounced by the teacher, as — 
"The ball is round;" ^' My ball is green;" 
"All these balls are made of rubber," &c. 
They are then required to return all, except 
the blue balls, those who give up theirs being 
allowed to select from the box a blue ball in 



exchange ; so that in the end each child has 
a ball of that color. The teacher then says : 
" Each of you has now a blue, rubber ball, 
which is round, soft,znd light; and these balls 
will be your balls to play with. I will give 
you another ball to-morrow, and the next day 
another, and so on, until you have quite a 
number of balls, all of which will be of rub- 
ber, but no two of the same color." 

The six differently colored balls are to be 
used, one on each day of the week, which 
assists the children in recollecting the days of 
the week, and the colors. After distributing 
the balls, the same questions may be asked as 
at the beginning, and the children taught to 
raise and drop their hands with the balls in 
them ; and if there is time, they may make a 
few attempts to Uirow and catch the balls. 
This is enough for the first lesson ; and it will 
be sure to awaken enthusiasm and delight in 
die children. 

The object of the first occupation is to teach 
the children to distinguish between the right 
and the left hand, and to name the various 
colors. It may serve also to develop their 
vocal organs, and instaict them in the rules 
of politeness. How the latter may be accom- 
plished, even with such simple occupation as 
playing with balls, may be seen from the fol- 
lowing : 

In presenting the balls, pains should be 
taken to make each child extend the right 



GUIDE TO KINDER-GARTNERS. 



hand, and do it gracefully. The teacher, in 
putting the ball into the little outstretched 
hand, says : 

" Charles, I place this red (green, yellow, 
&c.,) ball into your right hand." The child 
is taught to reply — 

" I thank you, sir." 
After the play is over, and the balls are to 
be replaced, each one says, in returning his 
ball— 

" I place this red (green, yellow, &c.,) ball, 
with my right hand, into the box." 

When the children have acquired some 
knowledge of the different colors, they may 
be asked at the commencement : 

" With which ball would you like to play 
this morning — the green,, red, or blue one ? " 
The child will reply : 

" With the blue one, if you please ; " or one 
of such other color as may be preferred. 

It may appear rather monotonous to some 
to have each child repeat the same phrase ; 
but it is only by constant repetition and 
patient drill that anything can be learned 
accurately ; and it is certainly important that 
these youthful minds, in their formative state, 
should be taught at once the beauty of order 
and the necessity of rules. So the left hand 
should never be employed when tlie right 
hand is required; and all mistakes should 
be carefully noticed and corrected by the 
teacher. One important feature of this sys- 
tem is the inculcation of habits of precision. 

The children's knowledge of color may be 
improved by asking them what other things 
are similar to the different balls, in respect to 
color. After naming several objects, they 
may be made to repeat sentences like the fol- 
lowing : 

" My ball is green, like a leaf" " My ball 
is yellow, like a lemon." " And mine is red, 
like blood," &c. 

Whatever is pronounced in these conversa- 
tional lessons should be articulated very dis- 
tinctly and accurately, so as to develop the 
organs of speech, and to correct any defect 
of utterance, whether constitutional or the 



result of neglect. Opportunities for phonetic 
and elocutionary practice are here afforded. 
Let no one consider the infant period as too 
early for such exercises. If children learn to 
speak well before they learn to read, they 
never need special instruction in the art of 
reading with expression. 

For a second play with the balls, the class 
forms a circle, after the children have received 
the balls in the usual manner. They need to 
stand far enough apart, so that each, -with 
arms extended, can just touch his neighbor's 
hand. Standing in this position, and having 
the balls in their right hands, the children 
pass them into the left hands of their neigh- 
bors. In this way, each one gives and re- 
ceives a ball at the same time, and the left 
hands should, therefore, be held in such a 
manner that the balls can be readily placed 
in them. The arms are then raised over the 
head, and the balls passed from, the left into 
the right hand, and the arms again extended 
into the first position. This process is re- 
peated until the balls make the complete 
circuit, and return into the right hands of the 
original owners. The balls are then passed 
to the left in the same way, everything being 
done in an opposite direction. This exercise 
should be continued until it can be 3one 
rapidly and, at the same time, gracefully. 

Simple as this performance may appear to 
those who have never tried it, it is, neverthe- 
less, not easily done by very young children 
without frequent mistakes and interruptions. 
It is better that the children should not turn 
their heads, so as to watch their hands during 
the changes, but be guided solely by the sense ' 
of touch ; and to accomplish this with more 
certainty, they may be required to close their 
eyes. It is advisable not to introduce this 
play or any of the following, until expertness 
is acquired in the first and simpler form. 

In the third play, the children forrii in two 
rows fronting each other. Those of one row 
only receive balls. These they toss to the 
opposite row : first, one by one ; then two by 
two; finally, the whole row at once, always 



GUIDE TO KINDER-GARTNERS. 



to the counting of the teacher — "one, two, 
throw." 

Again, forming four rows, the children in 
the first row toss up and catch", tlien throw to. 
the second row, then to the third, then to the 
fourth, accompanying the exercise with count- 
ing as before, or with singing, as soon as this 
can be done. 

For a further variety, the balls are thrown 
upon the floor, and caught, as they rebound, 
with the rig/tt hand or the ic/t hand, or witli 
the hand inverted, or they may be sent back 
to the floor several times before catching. 

Throwing the balls against the wall, tossing 
them into the air, and many other exercises 



may be introduced whenever the balls are 
used, and will always serv-e to interest the 
children. Care should be taken to have every 
movement performed in perfect order, and that 
every child take part in all the exercises in its 
turn. 

At the close of every ball play, the children 
occupy their original places marked on the 
floor, the balls are collected by one or two of 
the older pupils, and after this has been done, 
each child takes the hand of its opposite 
neighbor, and bowing, says, " good morning," 
when they march by twos, accompanied by 
music, once or twice through the hall, and 
then to their seats for other occupation. 



THE SECOND GIFT. 



The Second Gift consists of a sphere, a 
cube, and a cylinder. These the teacher places 
upon the table, together with a rubber ball, 
and asks : 

" Which of these three objects looks most 
like theball?" 

The children will certainly point out the 
sphere, but, of course, without giving its name. 

" Of what is it made ?•" the teacher asks, 
placing it in the hand of some pupil, or rolling 
it across the table. 

The answer will doubtless be, " Of wood." 
" So we might call the object a wooden ball. 
But we will give it another name. We will 
call it a sphere." 

Each child must here be taught to pro- 
nounce the word, enunciating each sound very 
distinctly. The ball and sphere are then fur- 
ther compared with each other, as to material, 
color, weight, &c., to find their similarities 
and dissimilarities. Both are round; both 
roll. The ball is soft; the sphere is hard. 
The ball is light; the sphere is heaiiy. The 
sphere makes a louder noise when it falls from 



the table than the ball. The ball rebounds 
when it is thrown upon the floor ; the sphere 
does not. All these answers are drawn out 
from the pupils by suitable experiments and 
questions, and every one is required to repeat 
each sentence when fully explained. 

The children then form a circle, and the 
teacher rolls the sphere to one of them, ask- 
ing the child to stop it with both his feet. 
This child then takes his place in the center, 
and rolls the sphere to another one, who again 
stops it with his feet, and so on, until all the 
children have in turn taken their place in the 
center of the circle. At another time, the 
children may sit in two rows upon the floor, 
facing each other. A white and a black 
sphere are then given to the heads of the 
rows, who exchange by rolling them across to 
each other. Then the spheres are rolled 
across obliquely to the second individuals in 
the rows. These exchange as before, and 
then roll the spheres to those who sit third, 
and so on, until they have passed throughout 
the lines and back again to the head. Both 



GUIDE TO KINDER-GARTNERS. 



spheres should be rolling at the same instant, 
which can be effected only by counting or 
when time is kept to accompanying music. 

Another variety of play in the use of this 
gift consists in placing the rubber ball at a 
distance on the floor, and letting each child, 
in turn, attempt to hit it with the sphere. 

For the purpose of further instruction, the 
sphere, cube, and cylinder are again placed 
upon the table, and the children are asked 
to discover and designate the points of re- 
semblance and difference in the first two. 
They will find, on examination, that both are 
made of wood, and of the same color ; but 
the sphere can roll, while the cube cannot.. 
Inquire the cause for this difference, and the 
answer will, most likely, be either, " the sphere 
is round," or "the cube has corners." 

" How many corners has the cube ? " The 
children count them, and reply, " Eight." 

" If I put my finger on one of these comers, 
and let it glide down to the corner below it, 
(thus,) my finger has passed along an edge 
of the cube. How many such edges can we 
count on this cube? I will let my finger 
glide over the edges, one after the other, and 
you may count." 

"One, two, three, 12." 

"Our cube, then, has eight corners, and 
twelve edges. I will now show you four cor- 
ners and four edges, and say that this part 
of the cube, which is contained between these 
four corners and four edges, is called a side 
of the cube. Count how many sides the cube 
has." 

" One two, three, four, five, si.x." 

" Are these sides all alike, or is one small 
and another large ? " " They are all alike." 

" Then we may say that our cube has six 
sides, all alike, and that each side has four 
edges, all alike. Each of these sides of the 
cube is called a square.^' 

To explain the cylinder, a conversation like 
the following may take place. It will be ob- 
served that instruction is here given mainly 
by comparison, which is, in fact, tlie only 
philosophical method. 



The sphere, cube, and cylinder are placed 
together as before, in the presence of the 
children. They readily recognize and name 
the first two, but are in doubt about the third, 
whether it is a barrel or a wheel. They may 
be suffered to indulge their fancy for awhile 
in finding a name for it, but are, at last, told 
that it is a cyHnda; and are taught to pro- 
nounce the word distinctly and accurately. 

" What do you see on the cylinder which 
you also see on the cube ? " " The cylinder 
has two"sides." " Are the sides square, like 
those of the cube?" " They are not." 

But the cylinder can stand on these sides 
just as the cube can. Let us see if it cannot 
roll, too, as the sphere does. Yes ! it rolls ; 
but not like the- sphere, for it can roll only 
_in two ways, while the sphere can roll any 
way. So, you see, the sphere, cube, and 
cylinder are alike in some respects, and differ- 
ent in others. Can you tell me in what re- 
spects they are just alike?" 

" They are made of wood ; are smooth ; 
are of the same color; are heavy; make a 
loud noise when they fall on the floor." 

These answers must be drawn out by ex- 
periments with the objects, and by questions, 
logically put, so as to lead to these results as 
natural conclusions. The e.xercise may be 
continued, if desirable, by asking the children 
to name objects which look like the sphere, 
cube, or cylinder. The edge of a cube may 
also be explained as representing a straight 
line. The point where two or three lines or 
edges meet is called a corner; the inner 
point of a corner is an angle, of which each 
side, or square, of the cube has four. To 
sum up what has already been taught : The 
cube has six sides, or squares, all alike ; eight 
corners, and twelve edges ; and each side of 
the cube has four edges, all alike ; four cor- 
ners, and four angles. 

The sphere, cube, and cylinder, when sus- 
pended by a double thread, can be made to 
rotate around themselves, for the purpose of 
showing that the sphere appears the same in 
form in whatever manner we look at it ; that 



GUIDE TO KINDER-GARTNERS. 



the cube, when rotating, (suspended at the 
center of one of its sides,) shows the form 
of the cyhnder ; and that the cylinder, when 
rotating, (suspended at the center of its round 
side,) presents the appearance of a sphere. 

Thus, there is, as it were, an inner triunity 
in these three objects — sphere contained in 
cyhnder, and cylinder in cube, the cylinder 
forming the mediation between the two others, 
or the transition from one to the other. Al- 



though the child may not be told, the teacher 
may think, in this connection, of the natural 
law, according to which the fruit is contained 
in the flower, the flower is hidden in the bud. 
Suspended at other points, cylinder and 
cube present other forms, all of which are 
interesting for the children to look at, and can 
be made instructive to their young minds, if 
accompanied by apt conversation on the part 
of the teacher. 



THE THIRD GIFT. 



This consists of a cube, divided into eight 
smaller one-inch cubes. 

A prominent desire in the mind of ever)' 
child is to divide things, in order to examine 
the parts of which they consist. This natural 
instinct is observable at a very early period. 
The little one tries to change its toy by break- 
ing it, desirous of looking at its inside, and is 
sadly disappointed in finding itself incapable 
of reconstructing the fragments. Froebel's 
Third Gift is founded on this observation. 
In it the child receives a whole, whose parts 
he can easily separate, and put together again 
at pleasure. Thus he is able to do that which 
he could not in the case of the toys — restore 
to its original form that which was broken — 
making a perfect whole. And not only this — 
he can use the parts also for the construction 
of other wholes. 

The child's first plaything, or means of 
occupation, was the ball. Next came the 
sphere, similar to, yet so diflerent from, the 
ball. Then followed cube and cylinder, both, 
in some points, resembling the sphere, yet 
each having its own peculiaritiqg, which dis- 
tinguish it from the sphere and ball. The 
pupil, in receiving the cube, divisible into 
eight smaller cubes, meets with friends, and is 
delighted at the multiplicity of the gift. Each 



of the eight parts is precisely like the whole, 
except in point of size, and the child is im- 
mediately struck with this quality of his first 
toy for building purposes. By simply looking 
at this gift, the pupil receives the ideas of 
whole a.nd part — of form and cmnparative size ; 
and by dividing the cube, is impressed with 
the relation of one part to another in regard 
to position rfnd order of movements, thus 
learning readily to comprehend the use of 
such terms as above, below, before, behind, right, 
left, &c., &c. 

With this and all the following gifts, we 
produce what Froebel zaW^ forms of life, forms 
of knotuledge, and forms of beauty. 

The first are representations of objects which 
actually exist, and which come under our com- 
mon observation, as the works of human skill 
and art. The second are such as afford in- 
struction relative to number, order, proportion, 
&c. The third are figures representing only 
ideal forms, yet so regularly constructed as to 
present perfect models of symmetry and order 
in the arrangement of the parts. Thus in the 
occupations connected with the use of these 
simple building blocks, the child is led into 
the living world — there first to take notice of 
objects by comparison ; then to learn some- 
thing of their properties by induction, and 



GUIDE TO KINDER-GARTNERS. 



lastly, to gather into his soul a love and desire 
for the beautiful by the contemplation of those 
forms which are regular and symmetrical. 

THE PRESENTATION OF THE THIRD GIFT. 

The children having taken their usual seats, 
the teacher addresses them as follows : 

" To-day, we have something new to play 
with." 

Opening the package and displaying the 
box, he does not at once gratify their curiosity 
by showing them what it contains, but com- 
mences by asking the question — 

" Which one of the three objects we played 
with yesterday does this box look like?" 

They answer readily, " The cube." 

" Describe the box as the cube has been 
described, with regard to its sides, edges, 
corners, &c." 

If this is satisfactorily done, the cover may 
then be removed, and the box placed inverted 
upon the table. If the box is made of wood, 
it is placed upon its cover, wliich, when drawn 
out will allow the cubes to stand on the table. 
Lifting it up carefully, so that the contents may 
remain entire, the teacher asks : 

" What do you see now?" 

The answer is as before, " A cube." 

One of the scholars is told to push it across 
the table. In so doing, the parts will be likely 
to become separated, and that which was pre- 
viously whole will lie before them in fragments. 
The children are permitted to examine the 
small cubes ; and after each one of them has 
had one in his hand, the eight cubes are re- 
turned to the teacher, who remarks : 

" Children, as we have broken the thing, we 
must try to mend it. Let us see if we can put 
it together as it was before." 

This having been done, the boxes are then 
distributed among the children, and they are 
practiced in removing the covers, and taking 
out the cube without destroying its unity. 
They will find it difficult at first, and there 
will be many failures. But let them continue 
to try until some, at least, have succeeded, 
and then proceed to another occupation. 



PREPARATION FOR CONSTRUCTING 
FORMS. 

The surface of the tables is covered with a 
net-work of lines, forming squares of One inch. 
The spaces allotted to the pupils are separated 
from each other by heavy dark lines, and the 
centers are marked by some different color. 
In these first conversational lessons, the chil- 
dren must be taught to point out the right 
upper corner of their table space, the left 
upper, the right and left lower, the upper and 
lower edges, the right and left edges, and the 
center. With little staffs, or sticks cut at con- 
venient lengths, they may indicate direction, 
e. g., by laying them upon the table in a line 
from left to right, covering the center of the 
space, or extending them from the right upper 
to the left lower corner covering the center ; 
then from the middle of the upper edge to the 
middle of the lower edge, and so on. The 
teacher must be careful to use terms that can 
be easily comprehended, and avoid changing 
them in such a way as to produce any ambigu- 
ity in the mind of the child. 

Here, as in the more advanced exercises, 
everj'thing should be done with a great deal 
of precision. The children must understand 
that order and regularity in all the perform- 
ances are of the utmost importance. The 
following will serve as an illustration of the 
method : The children having received the 
boxes, they are required to place them exactly 
in the center of their spaces, so as to cover 
four squares. They then take hold of the box 
with the left hand, and remove the cover with 
the right, placing it by the right upper corner 
of the net-work on the table. They next 
place the left hand upon the open box, and 
reverse it with the right hand, so that the left 
is on the table. Drawing it carefully from 
beneath, they let the inverted box rest on the 
squares in the center. The right hand is used 
to raise the bpx carefully from its place, and, 
if successful, eight small cubes will stand in 
the center of the space, forming one large 
cube. Lastly, the box is placed in the cover 
at the right Upper corner, and care should 



GUIDE TO KINDER-GARTNERS. 



be taken that all are arranged in exact posi- 
tion. 

(If the cubes are enclosed in wooden boxes 
with covers to be drawn out at the side, these 
manipulations are to be changed accordingly.) 

At the close of any play, when the ma- 
terials are to be returned to the teacher, the 
same minuteness of detail must be observed. 

Replacing the box over the cubes, placing 
the left hand beneath, and lifting the box with 
the right, reversing it, and placing it again 
upon the center of the table, then covering 
it — these are processes which must be re- 
peated many times before the scholar can 
acquire such expertness as shall render it 
desirable to proceed to the real building occu- 
pation. 

FORMS OF LIFE. 

The boxes being opened as directed, and 
the cubes upon the center squares — in each 
space — the question is asked : 

" How many little cubes are there ? " 
" Eight." 

" Count them, placing them in a row from 
left to right," (or from right to left.) 

" What is that.' " " A row of cubes." 

It may bear any appropriate name which 
the children give it — as "a train of cars," "a- 
company of soldiers," " a fence," &c. 

" Now count your cubes once more, placing 
them one upon another. What have you 
there ? " 

" An upright row of eight cubes." 

"Have you ever seen anything standing 
like this upright row of cubes ? " 

" A chimney." " A steeple." 

" Take down your cubes, and build two 
upright rows of them — one square apart. 
What have you now ? " 

" Two little steeples," or " two chimneys." 
Thus, with these eight cubes, many forms of 
life can be built under the guidance of the 
teacher. It is an important rule in this occu- 
pation, that nothing should be rudely destroyed 
which has been constructed, but each new form 
is to be produced by slight change of the pre- 
ceding one. 



On Plates I. and II., a number of these are 
given. They are designated by Froebel as 
follows : 

1. Cube, or Kitchen Table. 

2. Fire-Place. 

3. Grandpa's Chair. 

4. Grandpa's and Grandma's Chairs. 

5. A Castle, with two towers. 

6. A Stronghold. 

7. A Wall. 

8. A High Wall. 

9. Two Columns. 

10. A Large Column, with two memorial 
stones. 

11. Sign-Post. 

12. Cross. 

13. Two Crosses. 

14. Cross, with pedestal. 

15. Monument. 

16. Sentry-Box. 

17. A Well. 

18. City Gate. 

19. Triumphal Arch. 

20. City Gate, with Tower. 

21. Church. 

22. City Hall. 

23. Castle. 

24. A Locomotive. 

25. A Ruin. 

26. Bridge, with Keeper's House. 

27. Two Rows of Trees. 

28. Two Long Logs of Wood. 

29. A Bole. 

30. Two Small Logs of Wood. 

31. Four Garden Benches. 

32. Stairs. 

33. Double Ladder. 

34. Two Columns on Pedestals. 

35. Well-Trough. 

36. Bath. 

37. A Tunnel. 

38. Easy Chair. 

39. Bench, with back. 

40. Cube. 

Several of the names in this list represent 
objects which, being more specifically German, 
will not be recognized by the children. Ruins, 



14 



GUIDE TO KINDER-GARTNERS. 



castles, sentry-boxes, sign-posts, perhaps they 
have never aeen ; but it is easy to tell them 
something about these objects which will in- 
terest them. They will listen with pleasure 
to short stories, narrated by way of explana- 
tion, and thus associating the story with the 
form, be able, at another time, to reconstruct 
the latter while they repeat the former in their 
own words. It is not to be expected, how- 
ever, that teachers in this country should 
adhere closely to the list of Froebel. They 
may, with advantage, vary the forms, and, if 
they choose, affix other names to those given 
upon the plates. It is well sometimes to 
adopt such designations as are suggested by 
the children themselves. They will be found 
to be quite apt in tracing resemblances be- 
tween their structures and the objects with 
which they are familiar. 

In order to make the occupation still more 
useful, they should be required also to point 
out the dissimilarities existing between the 
form and that which it represents. 

It is proper to allow the child, at times, to 
invent forms, the teacher assisting the fantasy 
of the little builder in the work of construct- 
ing, and in assigning names to the structure. 
When a figure has been found, and named, 
the child should be required to take the blocks 
apart, and build the same several times in suc- 
cession. Older and more advanced scholars 
suggest to younger and less abler ones, and 
the latter will be found to appreciate such 
help. 

It is a common observation, that the younger 
children in a family develop more rapidly than 
the older ones, since the former are assisted 
in their mental growth by companionship with 
the latter. This benefit of association is seen 
more fully in the Kinder-Garten, under the 
judicious guidance of a teacher who knows 
how to encourage what is right, and check 
what is wrong, in the disposition of the chil- 
dren. 

It should be remarked, in connection with 
these directions, that in the use of this and 
the succeeding gift it is essential that all the 



blocks should be used in the building of each 
figure, in order to accustom the child to look 
upon things as mutually related. There is 
nothing which has not its appointed place, 
and each part is needed to constitute the 
whole. For example, the well-trough (35) 
may be built of six cubes, but the remaining 
two should represent two pails with which the 
water is conveyed to the trough. 

FORMS OF KNOWLEDGE. 

These do not represent objects, either real 
or ideal. They instruct the pupil concerning 
the properties and relations of numbers, by 
a particular arranging and grouping of the 
blocks. Strictly speaking, the first effort to 
count, by laying them on the table one after 
another, is to be classed under this head. . 
The form thus produced, though varied at 
each trial, is one of the forms of knowledge, 
and by it the child receives its first lesson in 
arithmetic. 

Proceeding further, he is taught to add, 
always by using the cubes to illustrate the 
successive steps. Thus, having placed two 
of the blocks at a little distance from each 
other on the table, he is caused to repeat, 
" One and one are two." Then placing 
another upon the table, he repeats, " One 
and two are three," and so on, until all the 
blocks are added. 

Subtraction is taught in a similar manner. 
Having placed all the cubes upon the table, 
the scholar commences taking them off, one 
at a time, repeating, as he does this, " One 
from eight leaves seven; "One from seven 
leaves six," and so on. 

According to circumstances, of which the 
Kinder-Gartner, of course, will be the best 
judge, these exercises may be continued fur- 
ther, by adding and subtracting two, three, 
and so on ; but care should always be taken 
that no new step be made until all that has 
j gone before is perfectly understood. 

With the more advanced classes, exercises 
in multiplication and division may be tried, 
by grouping the blocks. 



GUIDE TO KINDER-GARTNERS. 



15 



The division of the large cube, to illustrate 
the principles of proportion, is an interesting 
and instructive occupation ; and we will here 
proceed to give the method in detail. 

The children have their cube of eight be- 
fore them on the table. The teacher is also 
furnished with one, and lifting the upper half 
in the manner shown on Plate III., No. 4, 
asks: 

" Did I take the whole of my cube in my 
hand, or did I leave some of it on the table ? " 

" Yoii left some on the table." 

" Do I hold in my hand more of my cube 
than I left on the table, or are both parts 
alike .' " 

" Both are alike." 

" If things are alike, we call them equal. 
So I divided my cube into two equal parts, 
and each of these equal parts I call a half. 
Where are the two halves of my cube ? " 

" One is in your hand ; the other is on the 
table." 

" So I have two half cubes. I will now 
place the half which I have in my hand upon 
the half standing on the table. What have I 
now ? " 

" A whole cube." 

The teaclier, then separating the cube again 
into halves, by drawing four of the smaller 
cubes to the right and four to the left, as is 
indicated on Plate III., No. 2, asks : 

" What have I now before me ? " 

" Two half cubes." 

" Before, I had an upper and a lower half. 
Now, I have a right and a left half. Uniting 
the halves again I have once more a whole." 

The scholars are taught to repeat as fol- 
lows while the teacher divides and unites the 
cubes in both ways, and also as represented 
by Form No. 3 : 

" One whole — two halves." 

"Two halves — one whole." 

Again, each half is divided, as shown in 
Forms No. 5, 6, and 7. and the children are 
required to repeat during these occupations : 

" One whole — two halves." 

"One half — two quarters (or fourths.)" 



"Two quarters — one half." 

"Two halves — one whole." 

After these processes are fully explained, 
and the principles well understood by the 
scholars, they are to try their hand at divid- 
ing of the cube — first, individually, then all 
together. If they succeed, they may then be 
taught to separate it into eighths. It is not 
advisable, in all cases, to proceed thus far. 

Children under four years of age should be 
restricted, for the most part, to the use of the 
cubes for practical building purposes, and for 
simpler forms of knowledge. 

FORMS OF BEAUTY. 

Starting with a few simple arrangements, 
or positions, of the blocks, we are able to 
develop the forms contained in this class by 
means of a fixed law, viz., that every change 
of position is to be accompanied by a cor- 
responding movement on the opposite side. 
In this way symmetrical figures are construct- 
ed in infinite variety, representing no real 
objects, yet, by their regularity of outline, 
adapted to please the eye, and minister to a 
correct artistic taste. The love of the beau- 
tiful cannot fail to be awakened in the youth- 
ful mind by such an occupation as this, and 
with this emotion will be associated, to some 
extent, the love of the good, for they are in- 
separable. 

The works of God are characterized by 
perfect order and symmetry, and his good- 
ness is commensurate with the beauty mani- 
fest everj-where in the fruits of his creative 
power. The construction of forms of beauty 
with the building blocks will prepare the child 
to appreciate, by and by, the order that rules 
the universe. 

By Plates IV. and V. it will be seen that 
these forms are of only one block's height, 
and, consequently, represent outlines of sur- 
faces. It is necessarj' that the children should 
be guided, in their construction, by an easily 
recognizable center. Around this visible point 
all the separate parts of the form to be created 
must be arranged, just as in working out the 



i6 



GUIDE TO KINDER-GARTNERS. 



highest destiny of man, all his thoughts and 
acts need to be regulated by an invisible cen- 
ter, around which he is to construct a har- 
monious and beautiful whole. 

In order to produce the varied forms of 
beauty with the simple material placed in the 
hands of the scholar, he must first learn in' 
what ways two cubes may be brought in con- 
tact with each other. Four positions are 
shown on Plate IV. The blocks may be ar- 
ranged either — side by side, as in Fig. i ; edge 
to edge, as in Fig. 2 ; or edge to side, and side 
to edge, as in Nos. 3 and 4. Nos. i and 3 are 
the opposites to 2 and 4. Other changes of 
position may be made. For example, in Fig. i 
the block marked a may be placed above or to 
the right or to the left of the block marked b. 
The cubes may also be placed in certain rela- 
tions to each other on the table, without being 
in actual contact. These positions should be 
practiced perseveringly at the outset, so as to 
furnish a foundation for the processes of con- 
struction which are to follow. It is one of the 
important features of Froebel's system, that it 
enables the child readily to discover, and 
critically to observe, all relations which ob- 
jects sustain to one another. Thoroughness, 
therefore, is required in all the details of these 
occupations. 

We start from any fundamental form that 
may present itself to our mind. Take, for 
illustration, Form No. 5. Four cubes are 
here united side to side, constituting a square 
surface, and the outline is completed by plac- 
ing the four remaining cubes severally side to 
side with this middle square. In 6, edge 
touches edge ; in 7, side touches edge, and in 



8, edge touches side midway. Another mode 
of development is shown in Forms 9 — 15. 

The four outside cubes move toward the 
right by a half cube's length, until the original 
form reappears in No. 15. 

Now, the four outside cubes occupy the 
opposite position. Fig. 16, edges touch sides. 
They are moved as before, by a half cube's 
length, until, in Form No. 22, the one with 
which we started, is regained. 

We now extract the inside cubes (^), Fig. 
23, and each of them travels around its neigh- 
bor cube (a), until a standing, hollow square 
is developed, as in Fig. 29. 

Now cube a again is set in motion. It 
assumes a slanting direction to the remain- 
ing cubes. Fig. 30, and, pursuing its course 
around them, the Form, No. 29, reappears 
in No. 36. 

Next, b is drawn out. Fig. 37, and a pushed 
in, until a standing cross is formed. Fig. 38, 
b, constantly traveling on by a half cube's 
length, until. Fig. 43, all cubes are united in a 
large square, and b again begins traveling, by 
a cube's length, turning side to side and edge 
to edge. In Fig. 48, b performs as a has 
done. 

But with more developed children we may 
proceed on other principles, Fig. 49, intro- 
ducing changes only on two instead of four 
sides, and thus arriving successively at Forms 
50 — 60. 

After each occupation, the scholars should 
replace their cubes in the boxes, as heretofore 
described, and the material should be re- 
turned to the closet where it is kept before 
commencing any other play. 



THE FOURTH GIFT. 



The preceding gift consisted of cubical 
blocks, all of their three dimensions being the 
same. In the Fourth Gift, we have greater 
variety for purposes of construction, since each 
of the parts of the large cube is an oblong, 
whose length is twice its width, and four times 
its thickness. The dimensions bear the same 
proportion to each other as those of an or- 
dinary brick ; and hence these blocks are 
sometimes called bricks. . They are useful in 
teaching the child difference in regard to 
length, breadth, and height. This difference 
enables them to construct a greater variety 
of forms than he could by means of the third 
gift. By these he is made to understand, 
more distinctl)', the meaning of the terms per- 
pendicular and horizontal. And if the teacher 
sees fit to pursue the course of experiment 
sufficiently far, many philosophical truths will 
be developed ; as. for instance, the law of 
equilibrium, shown by laying one block across 
another, or the phenomenon of continuous 
motion, exhibited in the movement of a row 
of the blocks, set on end, and gently pushed 
from one direction. 

PREPARATION FOR CONSTRUCTING 
FORMS. 

This gift is introduced to the children in a 
manner similar to the presentation of the third 
gift. The cover is removed, and the box is 
reversed upon the table. Lifting the box 
carefully, the cube remains entire. The chil- 
dren are made to observe that, when whole, 
its size is the same as that of the previous one. 
Its parts, however, are very different in form, 
though their number is the same. There are 
still eight blocks. Let the scholars compare 
one of the small cubes of the third gift with 
one of the oblongs in this gift ; note the simi- 
3 



larities and the differences ; then, if they can 
comprehend that notwithstanding they are so 
unlike m /arm. their solid contents is the same, 
since it takes just eight of each to make the 
same sized cube, an important lesson will 
have been learned. If told to name objects 
that resemble the oblong, they will readily 
designate a brkk^ table, piano, closet, &c., and 
if allowed to invent forms of life, will, doubt- 
less, construct boxes, benches, &c. 

The same precision should be observed in 
all the details of opening and closing the 
plays with this gift as in those previously de- 
scribed. 

FORMS OF LIFE. 

The following is a list of Froebel's forms, 
which are represented on Plates VI. and VII. 
If the names do not appear quite striking, or 
to the point, the teacher may try to substitute 
better ones : 

1. The Cube. 

2. Part of a Floor, or Top of a Table. 

3. Two Large Boards. 

4. Four Small Boards. 

5. Eight Building Blocks. 

6. A Long Garden Wall. 

7. A City Gate. 

8. Another City Gate. 

9. A Bee Stand. 

10. A Colonnade. 

11. A Passage. 

12. Bell Tower. 

13. Open Garden House. 

14. Garden House, with Doors. 

15. Shaft. 

16. Shaft. 

17. A Well, with Cover. 

18. Fountain. 

19. Closed Garden Wall. 



18 



GUIDE TO KINDER-GARTNERS. 



20. An Open Garden. 

21. An Open Garden. 

22. Watering-Trough. 

23. Shooting-Stand. 

24. Village. 

25. Triumphal Arch. 

26. Caroussel. 

27. Writing Desk. 

28. Double Settee. 

29. Sofa. 

30. Large Garden Settee. 

31. Two Chairs. 

32. Garden Table Chairs. 

33. Children's Table. 

34. Tombstone. 

35. Tombstone. 

36. Tombstone. 

37. Monument. 

38. Monument. 

39. Winding Stairs. 

40. Broader Stairs. 

41. Stalls. 

42. A Cross Road. 

43. Tunnel. 

44. Pyramid. 

45. Shooting-Stand. 

46. Front of a House. 

47. Chair, with Footstool. 

48. A Throne. 

49. f Illustration of 

50. \ Continuous Motion. 

Here, as in the use of tlie previous gift, 
one form is produced from another by slight 
changes, accompanied by explanations on the 
part of the teacher. Thus, Form 30 is easily 
changed to 31, 32, and ^3, and Form 34 may 
be changed to 35, 36, and 37. In every case, 
all the blocks are to be employed in con- 
structing a figure. 

FORMS OF KNOWLEDGE. 
This gift, like the preceding, is used to 
communicate ideas of divisibility. Here, how- 
ever, on account of the particular form of 
the parts, the processes are adapted rather to 
illustrate the division of a surface, than of a 
solid body. 



The cube is first arranged so that one per- 
pendicular and three horizontal cuts appear, 
aiid a child is then requested to separate it into 
halves, these halves into quarters, and these 
quarters into eighths. Each of the latter will 
be found to be one of the oblong blocks, and 
this for the time, may be made the subject of 
conversation. 

" Of what material is this block made ? " 

"What is the color?"- 

"What objects resemble it in form?" 

" How many sides has it?" 

" Which is the largest side ? " 

"Which is the smallest side?" 

" Is there a side larger than the smallest 
and smaller than the largest?" 

In this way, the scholars learn that there 
are three kinds of sides, symmetrically arrang- 
ed in pairs. The upper and lower, the right 
and left, the front and back, are respectively 
equal to and like each other. 

By questions, or by direct explanation, facts 
like the following, may be made apparent to 
the minds of children. "The upper and low- 
er sides of the block are twice as large as the 
two long sides, or the front and back, as they 
may be called. Again, the front and back are 
twice as large as the right and left, or the two 
short sides of the block. Consequently, the 
two largest sides are four times as large as 
the two smallest sides." This can be demon- 
strated in a very interesting way, by placing 
several of the blocks side by side, in a varie- 
ty of positions, and in all these operations 
the children should be allowed to experiment 
for themselves. The small cubes of the pre- 
ceding gift may also with propriety be brought 
in comparison with the oblongs of this gift, and 
the differences observed. 

When the single block has been employed 
to advantage, through several lessons, the 
whole cube may then be made use of, for the 
representation of forms of knowledge. 

Construct a tablet or plane as in Plate VIII. 
a. In order to show the relations of dimen- 
sion, divide this plane into halves, either by a 
perpendicular or horizontal cut (b and c). 



GUIDE TO KINDER-GARTNERS. 



19 



These two forms will give rise to instruct- 
ive observations and remarks by asking : 

" What was the form of the original tablet?" 

"What is the form of its halves? " 

" How many times larger is their breadth 
than their height ? " 

So with regard to the position of the oblong 
halves ; the one at b may be said to be lying 
while that at c is statiding. 

" Change a lying to a standing oblong." In 
order to do this, the child will move the first 
so as to describe a quarter of a circle to the 
right or left. 

"Unite two oblongs by joining their small 
sides. You then have a large lying oblong "(f). 

"Separate again (/) and divide each part 
into halves, (;'). You have now four parts 
called quarters, and these are squares, in their 
surface form." 

Each of these quarters may be subdivided, 
and the children taught the method of division 
by two. Other material may also be used in 
connection with the blocks, such as apples, or 
any small objects which serve to illustrate the 
properties of number. It is evident that these 
operations should be conducted in the most 
natural way, and never begun at too early a 
stage of development of the little ones. In 
figures e, g, h and k on Plate VIII. another 
mode is indicated, for the purpose of illus- 
trating further the conditions of form connect- 
ed with this gift. Figs, i— 16 Plate VIII. 
show the manner in which exercises in addition 
and subtraction may be introduced, as has al- 
ready been alluded to in the description of the 
Third Gift. 

FORMS OF BEAUTY. 
We first ascertain, as in the case of the 
cubes, the various modes in which the oblongs 
can be brought in relation to each other. 
These are much more numerous than in the 
Third Gift, because of the greater variety in 



the dimensions of the parts. Plate IX. shows 
a number of forms of beauty derivable from 
the original form, I. Each two blocks form 
a separate group, which four groups touching 
in the center, form a large square. The out- 
side blocks (a) move in Figs, i — 9, around the 
stationary middle. 

The inside blocks {b) are now drawn out 
(Fig. 10), then the blocks (a) united to form 
a hollow square (Fig. 11), around which b 
moves gradually (Figs. 12 and 13). 

Now b is combined into a cross with open 
center, a goes out (Fig. 14) and moves in an 
opposite direction until Fig. 17 appears. 

By extricating b the eight-rayed star (Fig. 
18) is formed. In Fig. 19 a revolves, b is 
drawn out until edge touches edge, and thus 
the form of a flower appears (Fig. 20). 

Now b is turned (Fig. 21), and in Fig. 22, 
a wreath is shown. In Fig. 22, the inside 
edges touch each other; in Fig. 23, inside 
and outside ; in Fig. 24, edges with sides, and 
b is united to a large hollow square, around 
which a commences a regular moving. In 
Fig. 29, a is finally united to a lying cross, and 
thereby another starting-point gained for a 
new series of developments. 

Each of these figures can be subjected to 
a variety of changes by simply placing the 
blocks on their long or short sides, or as the 
children will say, by letting them stand up or 
lie down. The net-work of lines on the 
table is to be the constant guide, in the con- 
struction of forms. In inventing a new series, 
place a block above, below, at the right or 
left of the center ; and a second opposite and 
equidistant. A third and a fourth are placed 
at the right and left of these, but in the same 
position relative to the center. The remain- 
ing four are placed symmetrically about those 
first laid. By moving the a's or Vf, regularly 
in either direction, a variety of figures may 
be formed. 



THE FIFTH GIFT. 

CUBE, TWICE DIVIDED IN EACH DIRECTION. 

(plates X. .TO XVI.) 



All gifts used as occupation material in the 
Kinder-Garten develop, as previously stated, 
one from another. The Fifth Gift, like that 
of the Third and Fourth Gifts, consists of a 
cube again, although larger than the previous 
ones. The cube of the Third Gift was divided 
mice in all directions. The natural progress 
from I is to 2 ; hence the cube of the Fifth 
Gift is divided twict in all directions ; conse- 
quently, in three equal parts, each consisting 
of 7iine smaller cubes of equal size. But as 
this division would only have multiplied, not 
diversified, the occupation material, it was 
necessary to introduce a new element, by 
subdividing some of the cubes in a slanting 
direction. 

We have heretofore introduced only perpen- 
dicular and horizontal lines. These opposites, 
however, require their mediate element, and 
this mediation was already indicated in the 
forms of life and of beauty of the Third and 
Fourth Gifts, when side and edge, or edge 
and side, were brought to touch each other. 
The slanting direction appearing there trans- 
itionally — occasionally — here, becomes per- 
manent by introducing the slanting line, sepa- 
rated by the division of the body, as a bodily 
reality. 

Three of the part cubes of the Fifth Gift 
are divided into half cubes, three others into 
quarter cubes, so that there are left twenty- 
one whole cubes of the twenty-seven, produced 
by the division of the cube mentioned before, 
and the whole Gift consists of thirty-nine sin- 
gle pieces. 

4 



It is most convenient to pack them in the 
box, so as to have all half and quarter cubes 
and three whole cubes in the bottom row, (see 
Plate XV., 1%) which only admits of separating 
the whole cube in the various ways required 
hereafter, as it will also assist in placing the 
cube upon the table, which is done in the 
same manner as described with the previous 
Gifts. 

The first practice with this Gift is like that 
with others introduced thus far. Led by the 
question of the teacher, the pupils state that 
this cube is larger than their other cubes; 
and the manner in which it is divided will 
next attract their attention. They state how 
many times the cube is divided in each "direc- 
tion, how many parts we have if we separate 
it according to these various divisions, and 
carrying out what we say, gives them the 
necessary assistance for answering these ques- 
tions correcdy. In No. 3, Plate XV., the three 
parts of the cube have been laid side by side 
of each other. 

These three squares we can again divide 
in three parts, and these latter again in three, 
so that then we shall have twenty-seven parts, 
which teaches the pupil that 3X3=9-3X9 
= 27. 

To some, the repetition of the apparently 
simple e-xercises may appear superfluous ; but 
repetition alone, in this simple manner, will 
assist children to remember, and it is always 
interesting, as they have not to deal with ab- 
stractions, but have real things to look at for 
the formation of their conclusions. 



GUIDE TO KINDER-GARTNERS. 



But, again I say, do not continue these 
occupations any longer than you can com- 
mand the attention of your pupils by them. 
As soon as signs of fatigue or lackof interest 
become manifest, drop the subject at once, 
and leave the Gift to the pupils for their own 
amusement. If you act according to this ad- 
vice, your pupils never will over-e.xert them- 
selves, and will always come with enlivened 
interest to the same occupation whenever it 
is again taken up. 

After the children have become acquainted 
with the manner of division of their new 
large cube, and have exercised with it in the 
above-mentioned way, their attention is drawn 
to the shape of the divided half and quarter 
cubes. 

They are divided by means of slanting lines, 
which should be made particularly prominent, 
and the pupils are then asked to point out, 
on the whole cubes, in what manner they 
were divided in order to form half and quar- 
ter cubes. The pupils also point out hori- 
zontal, perpendicular and slanting lines which 
they observe in things in the room or other 
near objects. 

Take the two halves of your cube apart, 
and say, " How many corners and angles you 
can count on the upper and lower sides of 
these two half cubes?" "Three." Three 
corners and three angles, which latter, you 
recollect, are the insides of corners. We call, 
therefore, the upper and lower side of the 
half cube a triangle, which simply means a 
side or plane with three angles. The child 
has now enriched its knowledge of lines by 
the introduction of the oblique or slanting 
line, in addition to the horizontal and perpen- 
dicular lines, and of sides or planes by the 
introduction of the triangle, in addition to 
the square and oblong previously introduced. 
With the introduction of the triangle, a great 
treasure for the development of forms is 
added, on account of its frequent occurrence 
as elementary forms in all the many forma- 
tions of Tegular objects. 

The child is expected to know this Gift now 



sufficiently to employ it for the production 
of the various forms of life and beauty now 
to be introduced. 

FORMS OF LIFE. 
(plates X. AND XI.) 

The main condition here, as always, is 
that for each representation the whole of 
the occupation material be employed; not 
that only one object should always be built, 
but in such manner that remaining pieces 
be always used to represent accessory parts, 
although apart from, yet in a certain rela- 
tion to the main figure. The child should, 
again and again, be reminded that nothing 
belonging to a whole is, or could be, allowed 
to be superfluous, but that each individual 
part is destined to fill its position actively 
and effectively in its relation to some greater 
whole. 

Nor should it be forgotten that nothing 
should be destroyed, but everything produced 
by re-building. It is advisable always to start 
with the figure of the cube. 

There are only the few following models on 
our Plates lo and ii : 

1. Cube. 

2. Flower-Stand. 

3. Large Chair. 

4. Easy Chair, with Foot Bench. 

5. A Bed. Lowesfrow, fifteen whole cubes ; 
second row, six whole and six half cubes, com- 
posed of twelve quarter cubes; third row, six 
half cubes. 

6. Sofa. First row, sixteen whole and two 
half cubes ; 6°, ground plan. 

7. A Well. 7°, ground plan. 

8. House, with Yard. 8% ground plan ; 
twelve wTiole cubes, ground ; nine whole and 
six half cubes, second row ; roof, twelve quar- 
ter cubes. 

9. A Peasant's House. First row, ten 
whole cubes ; second row, eight whole and 
two half cubes; roof, eight cubes, three 
halves and two halves, and eight quarters 
and two halves and four quarters ; 9°, ground 
plan. 



GUIDE TO KINDER-GARTNERS. 



23 



10. School-House. Third row, three whole 
and six half cubes; fourth row, one whole 
and four quarter cubes ; 10°, ground plan. 

11. Church. Building itself. eighteen whole 
cubes ; roof, twelve quarter cubes ; steeple, 
four whole cubes and one half cube ; vestry, 
one whole and one half cube ; 1 1°, ground 
plan of Church. 

12. Church, with Two Steeples. Building 
itself, twelve whole cubes ; roof, twelve quar- 
ter cubes ; steeples, twice five whole cubes 
and one half cube ; between steeples, one 
whole cube ; 12", ground plan. 

13. Factory, with Chimney and Boiler- 
house. Factory, sixteen whole cubes; roof, 
six half and four quarter cubes ; chimney, five 
whole and two quarter cubes ; boiler-house, 
four quarter cubes ; roof, two quarter cubes ; 
13", ground plan. 

14. Chapel, with Hermitage. 

15. Two Garden Houses, with Rows of 
Trees. 

16. A Castle. 16", ground plan. 

17. Cloister in Ruins. 17°, ground plan. 

18. City Gate, with Three Entrances. 18°, 
ground plan. 

19. Arsenal. 19°, ground plan. 

20. City Gate, with Two Guard-Houses. 
20°, ground plan. 

21. A Monument. 21°, ground plan; first 
row, nine whole and four half cubes ; second 
to fourth row, each, four whole cubes ; on 
either side, two quarter cubes, united to a 
square column, and to unite the four columns, 
four quarter cubes. 

22. A Monument. 22°, ground plan; first 
row, nine whole and four quarter cubes ; sec- 
ond row, five whole and four half cubes ; third 
row, four whole cubes ; fourth row, four half 
cubes. 

23. A Large Cross. 23°, ground plan ; first 
row, nine whole and four times three quarter 
cubes ; second row, four whole cubes ; third 
row, four half cubes. 

Tables, chairs, sofas, beds, arc the first 
objects the child builds. They are the ob- 
jects with which it is most familiar. Then 



the child builds a house, in which it lives, 
speaking of kitchen, sleeping-room, parlor, 
and eating-room, when representing it. Soon 
the realm of its ideas widens. It roves into 
garden, street, &c. It builds the church, the 
school-house, where the older brothers and 
sisters are instructed ; the factory, arsenal, 
from which, at nooii and after the day's work 
is over, so many laborers walk out to their 
homes, to eat their dinner and supper, to 
rest from their work, and to play with their 
little children. The ideas which the children 
receive of all these objects by this occupa- 
tion, grow more correct by studying them in 
their details, where they meet with them in 
reality. In all this they are, as a matter 
of course, to be assisted by the instructive 
conversation of the teacher. It is not to be 
forgotten that the teacher may influence the 
minds of the children veiy favorably, by re- 
lating short stories about things and persons 
in connection with the object represented. 
Not their minds alone are to be -disciplined ; 
their hearts are to be developed, and each 
beautiful and noble feeling encouraged and 
strengthened. 

Be it remembered again that it is not neces- 
sary that the teacher should always follow the 
course of development shown in the pictures 
on our plates. Every course is acceptable, 
if only destruction is prevented and re-build- 
ing adhered to. Some of the pictures may 
not be familiar to some of the children. The 
one- has never seen a castle or a city gate, 
a well or a monument. Short descriptive 
stories about such objects will introduce the 
child into a new sphere of ideas, and stimu- 
late the desire to see and hear more and 
more, thus adding, daily and hourly, to the 
stock of knowledge of which he is already 
possessed. Thus, these plays will not only 
cultivate the manutil dexterity of the child, 
develop his eye, excite his fantasy, strengthen 
his power of invention, but the accompanying 
oral illustrations will also instruct him, and 
create in him a love for the good, the noble, 
the beautiful. 



24 



GUIDE TO KINDER-GARTNERS. 



The Fifth Gift is used with children from 
five to six years old, who are expected to be 
in their third year in the Kinder-Garten. 

A box, with its contents, stands on the 
table before each child. They empty the 
box, as heretofore described, so that the bot- 
tom row of the cube, containing the half and 
quarter cubes, is made the top row. 

" What have you now ? " 

" A cube." 

" We will build a church. Take off all 
quarter and half cubes, and place them on 
the table before you in good order. Move 
the three whole cubes of the upper row 
together, so that they are all to the left of 
the other cubes. Take three more whole 
cubes from the right side, and put them be- 
side the three cubes which were left of the 
upper row. Take the three remaining cubes, 
which were on the right side, and add them 
to the quarter and half cubes. What have 
you now ? " 

" A house without roof, three cubes high, 
three cubes long, and two cubes broad." 

" We will now make the roof Place on 
each of the six upper cubes a quarter cube 
with its largest side. Fill up the space be- 
tween each two quarter cubes with another 
quarter cube, and place another quarter cube 
on top of it. What have you now ? " 

" A house with roof." 

" How many cubes are yet remaining .? " 

" Three whole and six half cubes." 

" Take the whole cubes, and place them, 
one on top of the other, before the house. 
Add another cube, made of two half cubes, 
and cover the top with half a cube for a roof. 
What have you now .'' " 

" A steeple." 

'• We will employ the remaining three half 
cubes to build the entrance. Take two of the 
half cubes, form a whole cube of them, and 
place it on the other side of the house, op- 
posite the steeple, and lay upon it the last 
half cube as a roof. What have we built 
now ? " 

" A cliurch, with steeple and entrance." 



FORMS OF BEAUTY. 

If we consider that the Fifth Gift is put 
into the hands of pupils when they have 
reached the fifth year, with whom, conse- 
quently, if they have been treated rationally, 
the external organs, the limbs, as well as the 
senses, and the bodily mediators of all men- 
tal activity, the nerves, and their central organ, 
the brain, have reached a higher degree of 
development, and their physical powers have 
kept pace with such development, we may 
well expect a somewhat more extensive activ- 
ity of the pupils so prepared, and be justified 
in presenting to them work requiring more 
skill and ingenuity than that of the previous 
Gifts. 

And, in fact, the progress with these forms 
is apparently much greater than with the 
forms of life ; because here the importance 
of each of the thirty-nine parts of the cube 
can be made more prominent. He who is 
not a stranger in mathematics knows that the 
number of combinations and permutations of 
thirty-nine different bodies does not count by 
hundreds, nor can be expressed by thousands; 
but that millions hardly suffice to exhaust all 
possible combinations. 

Limitations are, therefore, necessary here ; 
and these limitations are presented to us in 
tiie laws of beauty, according to which the 
whole structure is not only to be formed har- 
moniously in itself, but each main part of it 
mast also answer the claims of symmetry. 
In order to comply with these conditions, it 
is sometimes necessary, during the process 
of building a Form of Beauty, to perform 
certain movements with various parts simul- 
taneously. In such cases it appears advis- 
able to divide the activity in its single parts, 
and allow the child's eye to rest on these 
transition figures, that it may become perfectly 
conscious of all changes and phases during 
the process of development of the form in 
question. This will render more intelligible 
to the young mind, that real beauty can only 
be produced when one opposite balances 
another, if the proportions of all parts are 



GUIDE TO KINDER-GARTNERS. 



25 



equally regulated by uniting them with one 
common center. 

Another limitation we find in the fact, that 
each fundamental form from which we start 
is divided in two main parts — the internal 
and the external— and that if we begin the 
changes or mutations with one of these oppo- 
sites, they are to be continued with it until a 
certain aim be reached. By this process cer- 
tain small series of building steps are created, 
which enable the child — and, still more, the 
teacher — to control the method according to 
which the perfect form is reached. 

" Each definite beginning conditions a cer- 
tain process of its own, and however much 
liberty in regard to changes may be allowed, 
they are always to be introduced within cer- 
tain limils only." 

Thus, tlie fundamental form conditions all 
the changes of the whole following series. 
All fundamental forms are distinct from each 
other by their different centers, which may be 
a square, (Plate XII., Fig. 9,) a triangle, 
(Plate XIV., Fig. 37,) a he.xagon, octagon, or 
circle. 

Before the real formation of figures com- 
mences, the child should become acquainted 
with the combinations in which the new forms 
of the divided cubes can be brought with 
each other. It takes two half cubes, forms 
of them a whole, and, being guided by the 
law of opposites, arrives at the forms repre- 
sented on Plate XII. — i to 8, and perhaps at 
others of less significance. 

The scries of figures on Plates XIIL, XIV., 
XV., arc all developed, one from another, as 
the careful observer will easily detect. As it 
would lead too far to show the gradual grow- 
ing of one from another, and all from a com- 
mon fundamental form, we will show only the 
course of development of Figures 9 to 14, on 
Plate XII. 

The fundamental form (Fig. 9) is a stand- 
ing square, formed of nine cubes, and sur- 
rounded by four equilateral triangles. 

The course of development starts from the 
center part. The four cubes a move exter- 



nally, (Fig. 10,) the four cubes li do the same, 
(Fig. II,) cubes a move farther to the corner 
of the triangles, (Fig. 12,) cubes i move to 
the places where cubes a were previously, 
(Fig. 13.) If all eight cubes continue their 
way in the same manner, we ne.xt obtain a 
form in which a and l> remain with their cor- 
ners on the half of the catheti ; then follows 
a figure like 13, different only in so far as a 
and -i^ have exchanged positions; then, in 
like manner, follow 12, 11, 10, and 9. 

We, therefore, discontinue the course. The 
internal cubes so far occupied positions that 
l> and iT turned corners, a and c sides towards 
each other. In Fig. 14, the opposite appears, 
/> and t: show each other sides, a and £ cor- 
ners. Thus, in Fig. 15, we reach a new 
fundamental form. Here, not the cubes of 
the internal, but those of the external tri- 
angles furnish the material for changing the 
form. 

It is not necessaiy that the teacher, by 
strictly adhering to the law of development, 
return to the adopted fundamental form. She 
may interrupt the course, as we have done, 
and continue according to new conditions. 
But however useful it may be to leave free 
scope to the child's own fantasy, we should 
never lose sight of Froebel's principle, to lead 
to Imnful action, to accustom to following a 
definite rule. Nor should we ever forget that 
the child can only derive benefit from its 
occupation, if we do not over-tax the measure 
of its strength and ability. The laws of for- 
mation should, therefore, always be as definite 
and distinct as simple. As soon as the child 
cannot trace back the way in which you have 
led it, in developing any of the forms of life 
or beauty ; if it cannot discover how it arrived 
at a certain point, or how to proceed from it, 
the moment has arrived when the occupation 
not only ceases to be useful, but commences 
to be hurtful, and we should always studiously 
avoid that moment. 

In order to facilitate the child's control of 
his activity, it is well to give the cubes, which 
arc, so to say, the representatives of the law 



26 



GUIDE TO KINDER-GARTNERS. 



of development, instead of the letters a, b, c, 
names of some children present, or of friends 
of the pupils. This enlivens the interest in 
their movements, and the children follow them 
with much more attention. 

FORMS OF KNOWLEDGE. 

(plates XV. AND XVI.) 

The representations of the forms of knowl- 
edge, to which the Fifth Gift offers oppor- 
tunity, is of great advantage for the develop- 
ment of the child. To superficial observers, 
it is true, it may appear as if Froebel not 
only ascribed too much importance to the 
mathematical . element to the disadvantage 
of others, but that mathematics necessarily 
require a greater maturity of understanding 
than could be found with children of the 
Kinder-Garten age. But who thinks of in- 
troducing mathematics as a science ? Many 
a child, five or six years of age, has heard 
that the moon revolves around the earth, that 
a locomotive is propelled by steam, and that 
lightning is the effect of electricity. These 
astronomical, dynamic and physical facts have 
been presented to him, as mathematical facts 
are presented to his observation in Froebel's 
Gifts. Most assuredly it would be folly, if one 
would introduce in the Kinder-Garten math- 
ematical problems in the usual abstract man- 
ner. In the KinderGarten, the child beholds 
the bodily representation of an expressed 
truth, recognizes the same, receives it without 
difficulty, without overtaxing its developing 
mind in any manner whatsoever. Whatever 
would be difficult for the child to derive from 
the mere word, nay, which might under cer- 
tain circumstances be hurtful to the young 
mind, is taught naturally and in an easy man- 
ner by the forms of knowledge, which thus 
become the best means of e-xercising the 
child's power of observation, reasoning, and 
judging. Beware of all problems and ab- 
stractions. The child builds, forms, sees, 
observes, compares, and then expresses the 
truth it has ascertained. By repetition, these 
truths, acquired by the observation of facts. 



become the child's mental property, and this 
is not to be done hurriedly, but during tlie 
last two years in the Kinder-Garten and 
afterwards in the Primary Department. 

The first seven forms of knowledge on 
Plate XV. show the regular divisions of the 
cube in three, nine and twentj'-seven parts, 
lu cither case, a whole cube was employed, 
and yet the forms produced by division are 
different. This shows that the contents may 
be equal, when forms are different (Figs. 2, 3, 
4, or 5 and 6). 

This difference becomes still more obvious 
if the three parts of Fig. 2, are united to a 
standing oblong, or those of Fig. 3 to a lying 
oblong, or if a single long beam is formed of 
Fig. 4. 

Take a cube, children, place it bc'fore you, 
and also a cube divided in two halves, and 
place the two halves with their triangular 
planes or sides, one upon another. 

These two halves united are just as large 
as the whole cube. 

But the two halves may be united, also, in 
other ways. They may touch each other with 
their quadratic and right angular planes. 

Represent these different ways of uniting 
the two halves of the cube simultaneously. 
Notwithstanding the difference in the forms, 
the contents of mass of matter remained the 
same. 

In a still more multiform manner, this fact 
may be illustrated with the cubes divided in 
four parts. Similar exercises follow now with 
the whole Gift, and the children are led to 
find out all possible divisions in two, three, 
four, five, nine and twelve equal parts (Figs. 
8 to 18). 

After each such division the equal parts 
are to be placed one upon another, for divid- 
ing and separating are always to be followed 
by a process of combining and re-uniting. 
The child thus receives every time, a trans- 
formation of the whole cube, representing the 
same amount of matter in various forms 
(Fig. 19-22). The child should also be al- 
lowed to compare with each other the various 



GUIDE TO KINDER-GARTNERS. 



27 



thirds, quarters, or sixths, into which whole 
cubes can be divided, as shown in Figs. 9, 
10, II, 12, or 14, 15 and 16. 

It is understood that all these exercises 
should be accompanied by the living word 
of the teacher ; for thereby, only, will the 
child become perfectly conscious of the ideas 
received from perception, and the opportunity 
is offered to perfect and multiply them. The 
teacher should, however, be carefuF not to 
speak too much, for it is only necessary to 
keep the attention of the pupil to the object 
represented, and to render impressions more 
vivid. 

The divisions introduced heretofore, are 
followed by representations of regular mathe- 
matical figures, (planes,) as shown in Figs. 
23-26. The manner in which one is formed 
from the preceding one is easily seen from 
the figures themselves. 

As mentioned before, part of the occupa- 
tion described in the preceding pages, is to 



be introduced in the Primary Department 
only, where it is combined with other inter- 
esting but more complicated exercises. Sim- 
ply to indicate how advantageously this Gift 
may be used for instruction in geometiy in 
later years, we have added the Figs. 30" and 
30'', the representation of which shows the 
child the visible proof of the well-known 
Pythagorean axiom, by which the theoretical, 
abstract solution of the same, certainly, can 
alone be facilitated. 

For the continuation of the exercises in 
arithmetic, begun with the previous Gifts, the 
cubes of the present one are of great use. 
Exercises in addition and subtraction are con- 
tinued more extensively, and by the use of 
these means, the child will be enabled to 
learn, what is usually called the multiplication 
table, in a much shorter time and in a much 
more rational way than it could ever be ac- 
complished by mere memorizing, without visi- 
ble objects. 



THE SIXTH GIFT. 

LARGE CUBE, CONSISTING OF DOUBLY DIVIDED OBLONGS. 

(plates XVII. TO XX.) 



As the Third and Fifth Gifts form an 
especial sequence of development, so the 
Fourth and Sixth are intimately connected 
with each other. The latter is, so to say, a 
higher potence of the former, permitting, the 
observation in greater clearness, of the quali- 
ties, relations, and laws, introduced previously. 

The Gift contains twenty-seven oblong 
blocks or bricks, of the same dimensions as 
those of the Fourth Gift. Of these twenty- 
seven blocks, eighteen are whole, six are 
divided breadthwise, each in two squares, 
and three by a lengthwise cut, each in t\vo 
columns ; altogether making thirty-six pieces. 



The children soon become acquainted with 
this Gift, as the variety of forms is much less 
than in the preceding one, where, by an ob- 
lique division of the cubes, an entirely new 
radical principle was introduced. 

It is here, therefore, mainly the proportions 
of size of the oblongs, squares, and columns 
contained in this Gift and the number of each 
kind of these bodies, about which the child 
has to become enlightened, before engaging 
in building — playing, creating — withthis new 
material. 

The cube is placed upon the table — all parts 
are disjoined — then equal parts collected 



2S 



GUIDE TO KINDER-GARTNERS. 



into groups, and the child is then asked, 
"How many blocks have you altogether?" 
How many oblongs? how many squares? 
how many columns ? Compare the sides of 
the blocks with another — take an oblong — 
how many squares do you need to cover it ? 
how many columns ? 

Place the oblong upon its long edge, now 
upon its shortest side — and state how many 
squares or columns you need in order to 
reach its height, in either case. Exercises of 
this kind will instruct the child sufficiently, 
to allow it to proceed, in a short time, to the 
individual creating, or producing occupation 
with this new Gift. 

FORMS OF LIFE. 

(PLATES XVri. AND XVIH.) 

It is the forms of life, particularly, for 
which this Gift provides material, far better 
fitted, than any previously used. The ob- 
longs admit of a much larger extension of 
the plane, and allow the enclosure of a much 
more extensive hollow space, than was possi- 
ble, for instance, with the cubes of the Fifth 
Gift. Innumerable forms can therefore be 
produced with this Gift, and the attention and 
interest of the pupil will be constantly in- 
creased. 

This very variety, however, should induce 
the careful teacher to prevent the child's 
purely accidental production of forms. It is 
always necessary to act according to certain 
rules and laws, to reach a certain aim. The 
established principle, that one form should al- 
ways be derived from another, can be carried 
out here only with great difficulty, owing to 
the peculiarity of the material. It is therefore 
frequently necessary, particularly with the 
more complicated structures, to lay an entirely 
new foundation for the building to be erected. 

It is necessary, at all times, to follow the 
child in his operations, — his questions should 
always be answered and suggestions made to 
enlarge the circle of ideas. 

It affords an abundance of pleasure to a 
child to observe that we understand it and 



its work ; it is, therefore, a great mistake in 
education to neglect to enter fully into the 
spirit of the pupil's sphere of thinking and 
acting; and if we ever should allow our- 
selves to go so far as to ridicule his pro- 
ductions, instead of assisting him to improve 
on them, we would certainly commit a most 
fatal error. 

The selections of forms of life on Plates 
XVII. and XVIII., nearly all of which are 
in the meantime forms of art and knowledge, 
because of their architectural fundamental 
forms, and the mathematical proportions of 
their single parts, can, therefore, not fail to 
give nourishment to various powers of the 
mind. 

1. House without roof; back wall has no 
door, i", ground plan. 

2. Colonnade ; lowest row, five oblongs 
laid lengthwise, and back wall consisting of 
ten standing oblongs, upon which ten squares. 
2', ground plan. 

3. Hall, with columns. 

4. Summer House. 4% ground plan ; ves- 
tibule formed by six columns. 

5. Memorial Column of the Three Friends. 
5°, ground plan. 

6. Monument in Honor of "Some Fallen 
Hero. 6°, ground plan; lowest row, eight 
oblongs ; second square of nine squares, par- 
tially constructed of oblongs ; third, four sin- 
gle squares ; then four columns, four single 
squares, square of nine squares, square of 
four squares, etc. 

7. Facade of a Large House. 7°, ground 
plan. 

8. The Columns of the Three Heroes. 
8% ground plan. 

9. Entrance to Hall of Fame. 9°, ground 
plan ; first row, sLx squares and six oblongs ; 
second row, six oblongs ; third row, six 
squares, etc. 

10. Two Story House, with yard. io% 
ground plan. Io^ side view. 

11. Faqade. II^ ground plan. 

12. Covered Summer House. 12°, ground 
plan. 



GUIDE TO KINDER-GARTNERS. 



29 



13. Front View of a Factory. 13°, ground 
plan. I3^ side view. 

14. Double Colonnade. 14°, ground plan. 

15. An Altar. 15°, ground plan. 

16. Monument. 16°, ground j^lan. 

17. Columns of Concord. 17", ground 
plan. 

The fantasy of the child is inexhaustibly 
rich in inventing new forms. It creates gar- 
dens, yards, stables with horses and cattle, 
household furniture of all kinds, beds with 
sleeping brothers and sisters in them, tables, 
chairs, sofas, etc., etc. 

If several children combine their individual 
building they produce large structures, perfect 
barn-yards with all out-buildings in them, nay, 
whole villages and towns. The ideas that in 
union there is strength, and that by co-oper- 
ation great things may be accomplished, will 
thus early become manifest to the young 
mind. 

FORMS OF BEAUTY. 

(plates XIX. AND XX.) 

The forms of beauty of this Gift offer far less 
diversity than those of Gift No. 5 ; owing, how- 
ever, to the peculiar proportions of the plane, 
they present sufficient opportunity for charac- 
teristic representations, not to be neglected. 

We give on the accompanying plates a sin- 
gle succession of development of such forms. 
The progressive changes are easily recog- 
nized, as the oblong, which needs to be moved 
to produce the following figure, is always 
marked by a letter. The center-piece always 
consists of two of the little columns, standing 
one upon another, and important modifica- 



tions may be produced by using the oblongs 
in lying or standing positions. By employing 
the four little columns in various ways, many 
pleasant changes can be produced by them. 

FORMS OF KNOWLEDGE. 
(plate XX.) 

These also appear in much smaller num- 
bers compared with the richness and multi- 
plicity of the Fifth Gift. By the absence of 
oblique (obtuse and acute) angles, they are 
limited to the square and oblong, and exer- 
cises introduced with these previously, may 
be repeated here with advantage. 

All Froebel's Gifts are remarkable for the 
peculiar feature that they can be rendered ex- 
ceedingly instructive by frequently introduc- 
ing repetitions under varied conditions and 
forms, by which means we are sure to avoid 
that dry and fatiguing monotony which must 
needs result from repeating the same thing in 
the same manner and form. And still more, 
the child, thereby, becomes accustomed to 
recognize like in unlike, similarity in dissimi- 
larity, oneness in multiplicit}', and connection 
in the apparently disconnected. 

In Fig. 16-22, all squares that can be 
formed with the Sixth Gift are represented. 
In Fig. 23 we see a transition from the forms 
of knowledge to those of beauty. 

With the Sixth Gift we reach the end of 
the two series of development given by 
Froebel in the building blocks, whose aim 
is to acquaint the child with the general 
qualities of the solid body by own observa- 
tion and occupation with the same. 



THE SEVENTH GIFT. 

SQUARE AND TRIANGULAR TABLETS FOR LAYING OF FIGURES. 

(plates XXI. TO XXIX.) 



All mental development begins with con- 
crete beings. The material world with its 
multiplicity of manifestations first attracts 
the senses and excites them to activitj', thus 
causing the rudimental operations of the 
mental powers. Gradually — only after many 
processes, little defined and explained by any 
science as yet, have taken place — man be- 
comes enabled to proceed to higher mental 
activity, from the original impressions made 
upon his senses by the various surroundings 
in the material world. 

The earliest impressions, it is true, if often 
repeated, leave behind them a lasting trace 
on the m.ind. But between this attained pos- 
sibility to recall once-made observations, to 
represent the object perceived by our senses, 
by mental image (imagination), and the 
real thinking or reasoning, the real pure ab- 
straction, there is a very long step, and 
nothing in our whole system of education is 
more worthy of consideration than the sud- 
den and abrupt transition from a life in the 
concrete, to a life of more or less abstract 
thinking to which our children are submitted 
when entering school from the parental 
house. 

Froebel, by a long series of occupation * 
material, has successfully bridged over this 
chasm, which the child has to traverse, and 
the first place among it, the laying tablets of 
various forms occupy. 

The series of tablets is contained in five 
boxes containing— 

A. Quadrangular square tablets. 



B. Right angular (equal sides). ^ „ . 

C. Right angular (unequal sides). I . 

D. Equilateral, and {Tu^t 

E. Obtuse angular (equal sides). J 

The child was heretofore engaged with 
solid bodies, and in the representation of 
real things. It produced a house, garden, 
sofa, etc. It is true the sofa was not a sofa 
as it is seen in reality ; the one built by the 
child was, therefore, so to say, an image al- 
ready, but it was a bodily image, so much so 
that the child could place upon it 'a little 
something representing its doll. The child 
considered it a real sofa, and so it was to the 
child, fulfilling, as it did, in its little world, 
the purposes of a real sofa in real life. 

With the tablets, the embodied planes, the 
child can not represent a sofa, but a form 
similar to it ; an image of the sofa can be pro- 
duced by arranging the squares and triangles 
in a certain order. 

We shall see, at some future time, how 
Froebel continues on this road, progressing 
from the plane to the line, from the line to 
the point, and finally enables the child to 
draw the image of the object, with pencil or 
pen in his own little hand. 

A. THE QUADRANGULAR LAYING TAB- 
LETS (Squares). 

(PLATE XXI.) 

They are given the child first to the num- 
ber of six. In a similar way as was done 
with the various building gifts, the child is 
led to an acquaintance with the various quali- 



GUIDE TO KINDER GARTNERS. 



ties of Ihe new material, and to compare it, 
with other things, possessing similar qualities. 
It is advisable to let the child understand 
the connection existing between this and the 
previous gifts. The laying tablets are nothing 
but the embodied planes, or separated sides 
of the cube. Cover all the sides of a cube 
with square tablets and after the child has 
recognized the cube in the body thus formed, 
let it separate the tablets one by one, from 
the cube hidden by them. 

The following, or similar questions are here 
to be introduced : — What is the form of this 
tablet ? How many sides has it ? How 
many angles ? Look carefully at the sides. 
Are they alike or unlike each other? They 
are all alike. Now look at the corners. These 
also are all alike. Where have you seen sim- 
ilar figures ? 

What are such figures called ? Can you 
show me angles somewhere else ? Where 
the two walls meet is an angle. Here, there, 
and everywhere you find angles. 

But all angles are not alike, and they are 
therefore differently named. All these dif- 
ferent names you will learn successively, but 
now let us turn to our tablet. Place it right 
straight before you upon the table. Can you 
tell me now what direction these two sides 
have which form the angle ? The one is 
horizontal, the other perpendicular. An 
angle which is formed if a perpendicular 
meets a horizontal line, is called a right an- 
gle. How many of such angles can you 
count on your tablet? Four. Show me such 
right angles somewhere else. 

By the acquisition of this knowledge the 
child has made an important step forward. 
Looking for horizontal and perpendicular 
lines, and for right angles, it is led to investi- 
gate more deeply the relations of form, which 
it had heretofore observed only in regard to 
the size conditioned by it. 

The child's attention should be drawn to 
the fact that, however the tablet may be 
placed the angles always remain right angles 
though the lines are horizontal and perpen- 



dicular only in four positions of the tablet, 
namely, those where the edges of the tablet 
are placed in the same direction with the 
lines on the table before the child. This 
will give occasion to lead the child to a gen- 
eral perception of the standing or hanging of 
objects according to the plummet. 

But the tablet will force still another ob- 
servation upon the child. The opposite sides 
have an equal direction ; they are the same 
distance from each other in all their points ; 
they never meet, however many tablets the 
child may add to each other to form the lines. 

The child learns that such lines are called 
parallel lines. It has observed such lines 
frequently before this, but begins just now to 
understand their real being and meaning. 
It looks now with much more interest than 
ever before at surrounding tables, chairs, 
closets, houses, with their straight line orna- 
ments, for now the little cosmopolitan does 
not only receive the impressions made by the 
surroundings upon his senses, but he already 
looks for something in them, an idea of which 
lives in his mind. Although unconscious of 
the fact that with the right angle and the 
parallel line, h€< received the elements of 
architecture, it will pleasantly incite him to 
new observations whenever he finds them 
again in another object which attracts his 
attention. 

The teacher in remembrance of oar oft- 
repeated hints, will proceed slowly, and care- 
fully, according to the desire and need of the 
child. She repeats, explains, leads the child 
to make the same observations in the most 
different objects, and changing circumstances, 
or guides the child in laying other forms of 
knowledge (lying or standing parallelograms 
Fig. 4 and 5) of life, (steps. Fig. 6 and 8, 
double steps. Fig. 7 and 9, door, Fig. 10, sofa. 
Fig. II, cross. Fig. 12), or forms of beauty. 

The number of these forms is on the whole 
only very limited. It is well now to augment 
the number of tablets in the hands of the 
pupil, by two, when a much larger munber of 
forms can be produced. The various series 



32 



GUIDE TO KINDER GARTNERS. 



of forms of beauty, introduced with the third 
Gift, can be repeated here and enlarged upon, 
according to the change in tlie material now 
at the disposal of the child. 

B, RIGHT-ANGLED TRIANGLES. 
(PLATE XXI.) 

As from the whole cube, the divided cube 
was produced, so by division the triangle 
springs from the square. By dividing it 
diagonally in halves, we produce the rectan- 
gular triangle with equal sides. 

Although the form of the triangle was pre- 
sented to the child in connection with the 
Fifth Gift, it here appears more independentl)-, 
and it is not only on that account necessary 
to acquaint the child with the qualities and 
being of the new addition to its occupation 
material, but still more so as the forms of 
the triangles with which, as a natural sequence 
it will have to do hereafter, were entirely 
unknown to the pupil. The child places two 
triangles, joined to a square, upon the table. 

What kind of a line divides your four-cor- 
nered tablet.' An oblique or slanting line. 
In what direction does the line cut your 
square in two ? From the right upper corner 
to the left lower corner. Such a line we call 
a diagonal. 

Separate the two parts of the square, and 
look at each one separately. What do you 
call each of these parts ? What did you call 
the whole ? A square. How many corners 
or angles had the square ? Four. How many 
corners or angles has the half of the square 
you are looking at? Three. This half, 
therefore, is called a triangle, because, as I 
have explained to you before, it has three 
angles. How many sides has your tri- 
angle ? etc. 

Looking at the sides more attentively, 
what do you observe ? One side is long, the 
other two are shorter, and, like each other. 
These latter are as large as the sides of the 
square, all sides of which were alike. 

Now tell me what kind of angle it is, that 
is formed by these two equal sides ? It is a 



right angle. Why? and what will you call 
the other two angles ? How do the sides 
run which form these two angles ? They run 
in such a way as to form a very sharp point, 
and these angles are, therefore, called acute 
angles, which means sharp-pointed angles. 
Your triangle has then, how many different 
kinds of angles ? Two ; one right angle, and 
two acute angles. 

It is not necessary to mention that the 
above is not to be taught in one lesson. It 
should be presented in various conversations, 
lest the acquired knowledge might not be 
retained by even the brightest child. The 
attention of the pupil may also be led, in 
subsequent con\^ersations to the fact that the 
largest side is opposite the largest angle, and 
that the two acute angles are alike, etc. 
Sufficient opportunity for these and additional 
remarks will offer itself during the represen- 
tations of forms of life, of knowledge, and of 
beauty, for which the child will employ its 
tablets, according to its own free will, and 
which are not necessarily to be separated, 
neither here nor in any other part of these 
occupations, although it is well to observe a 
certain order at any time. 

Whenever it can be done, elementary knowl- 
edge may well be imparted, together with the 
representations of forms of life, and forms of 
beauty. 

In order to invent, the child must have 
observed the various positions which a trian- 
gle may occupy. It will find these acting 
according to the laws of opposites, already 
familiar to the child. 

The right angle, to the right below, (Fig. 17) 
it will bring into the opposite direction to the 
left above, (Fig. 18) then into the mediative 
positions to the left below, (Fig. 19) and to 
the right above, (Fig. 20). By turning, it 
comes aboi'e\h& long side, (Hypothenuse, Fig. 
21) then opposite below it, (Fig. 22) then to 
the right, (Fig. 23) and finally to the left of 
it, (Fig. 24). 

The various positions of two triangles are 
easily found by moving one of them around 



GUIDE TO KINDER-GARTNERS. 



33 



the other. Fig. 26-31 are produced from 
Fig. 25, by moving the triangle marked a, 
always keeping it in its original position, 
around the otlier triangle. 

In Figs. 32-37, the changes are produced, 
alternating regularly between a turn and a 
move of the triangle a. In Figs. 38-47, 
simply turning takes place. 

After the child has become acquainted with 
the first elements from which its formations 
develop, it receives for a beginning four of 
the triangled tablets. It then places the 
right angles together, and thereby forms a 
standing full square, (Fig. 48.) 

By placing the tablets in an opposite posi- 
tion', turning the right angles from within to 
without, it produces a lying square with the 
hollow in the middle, (Fig. 49). This hollow 
space has the same shape and dimensions as 
Fig. 48. The child will fancy Fig. 48 into the 
place of this hollow space, and will thereby 
transfer the idea of a full square upon an 
empty or hollow one, and will consequently 
make the first step from the perception of the 
concrete to its idea, the abstraction. 

The child will now easily find mediative 
forms between these two opposites. It places 
two right angles v.'ithin and two without, 
(Fig. 58 and 59) two above, and two below, 
(Fig. 50) two to the right, and two to the left, 
(Fig. 50- 

So far, two tablets always remained con- 
nected with one another. By separating 
them we produce the new mediative forms, 
52, 53, 54 and 55. in which again two and 
two are opposites. But instead of the right. 
the acute angles may meet in a point also, 
and thus Figs. 56 and 57 are produced, 
which are called rotation forms, because the 
isolated position of the right angle suggests, 
as it were, an inclination to fall, or turn, or 
rotate. 

The mediation between these two oppo- 
site figures is given in Figs. 50 and 5 1 — 
between them and Figs. 49 and 50 in Figs. 
58 and 59 ; and it should be remarked in 
this connection, that these opposites are con- 
5 



ditioned by the position of the right angle in 
all these cases. 

All these exercises accustom the pupil to a 
methodic handling of all his material. They 
develop a correct use of his eye, because 
regular figures will only be produced when 
his tablets are placed correctly and exactly 
in their places shown by the net-work on the 
table. The precaution which must be exer- 
cised by the child not to disturb the easily 
movable tablets, and the care employed to 
keep each in its place, are of the greatest 
importance for future necessary dexterity of 
hand. In a still greater degree than by these 
simple elementary forms just described, this 
will be the case, when the pupil comes into 
possession of the following boxes, containing 
a larger number — up to sixty-four — tablets for 
the formation of more complicated figures, 
according to the free exercise of his fantasy. 

FORMS OF LIFE. 
(plate xxiii.) 
All hints given in connection with the build- 
ing blocks, are also to be followed here, with 
this difference only, that we produce now . 
images of objects, whereas, heretofore, we 
united the objects themselves. 
The child here begins — 

A, WITH FOUR TABLETS. 

And forms witli them — 
I. A flower-pot. 2. A little garden-house. 
3. A pigeon-house. 

B, WITH EIGHT TABLETS. 

4. A cottage. 5. A canoe or boat. 6. 
A covered goblet. 7. A lighthouse. 8. A 
clock. 

C, WITH SI.XTEEN TABLETS. 

9. A bridge with two spans. 10. A large 
gate. II. A church. 12. A gate with bel- 
fry. 13. A fruit basket. 

D, WITH THIRTY-TWO TABLETS. 

14. A peasant's house. 15. A forge with 
high chimney. 16. .'\ coffee-mill. 17. A cof- 
fee-pot without handle. 



34 



GUIDE TO KINDER-GARTNERS. 



E, WITH SIXTY-FOUR TABLETS. 

i8. A two-Story house. 19. Entrance to a 
railroad depot. 20. A steamboat. 

In No. 21, we see the result of combined 
activity of many children. Although to some 
grown persons it may appear as if the images 
produced do not bear much resemblance to 
what they are intended to represent, it should 
be remembered that iu most cases, the chil- 
dren themselves have given the names to 
the representations. Instructive conversation 
should also prevent this drmvmg with planes, 
as it were, from being a mere mechanical pas- 
time ; the entertaining, living word must in- 
fuse soul into the activity of the hand and its 
creations. Each representation, then, will 
speak to the child and each object in the 
world of nature and art will have a story to 
tell to the child in a language for which it 
will be well prepared. 

We need not indicate how these conversa- 
tions should be carried on, or what they 
should contain. Who would not think, in 
connection with the pigeon-house, of the 
beautiful white birds themselves, and the nest 
they build ; the white eggs they lay, the ten- 
der young pigeons coming from them, and 
the care with which the old ones treat the 
young ones, until they are able to take care 
of themselves. An application of these re- 
lations to those between parents and children, 
and, perhaps, those between God and man, 
who, as his children enjoy his kindness and 
love every moment of their lives, may be 
made, according to circumstances — all de- 
pending on the development of the children. 
However, care should always be taken not to 
present to them, what might be called ab- 
stract morals, which the young mind is unable 
to grasp, and which, if thus forced upon it 
cannot fail to be injurious to moral develop- 
ment. The aim of all education should be 
love of the good, beautiful, noble, and sub- 
lime ; but nothing is more apt to kill this 
very love, ere it is born, than the monotony 
of dry, dull preaching of morals to young 
children. Words not so much as deeds — 



actual experiences in tiie life of the child, are 
its most natural teachers in this important 
branch of education. 

FORMS OF BEAUTY. 

(PLATES XXI. AND XXII.) 

Owing to the larger multiplicity of ele- 
mentary forms to be made with the triangles, 
the number of Forms of Beauty is a very large 
one. Triangle, square, right angle, rhomb, 
hexagon, octagon, are all employed, and the 
great diversity and beauty of the forms pro- 
duced lend a lasting charm to the child's 
occupation. Its inventive power and desire, 
led by law, will find constant satisfaction, and 
to give satisfaction in the fullest measure 
should be a prominent feature of all systems 
of education. 

FORMS TO BE BUILT WITH FOUR TABLETS 

have already been mentioned on page 33, as 
contained on Plate XXI — D, 48-59. We find 
more satisfaction by employing 

EIGHT TABLETS. 

In working with them, we can follow the 
most various principles. Series E, 60-69, is 
formed by doubling the forms produced by 
four tablets ; series F, starting from the fun- 
damental form 70, making one half of the 
tablets move from left to right, the length of 
one side, with each move. A new series 
would be produced, if we move from right to 
left in a similar manner. In these figures, 
sides always touch sides, and corners touch 
corners — consequendy, parts of the same kind. 

The transition or mediation between these 
two opposites, the touching of corners and 
sides, would be produced by shortening the 
movement of the traveling triangle one-half, 
permitting it to proceed one-half side only. 

But let us return to fundamental form 70. 
In it, either large sides (hypothenuses) or 
small sides (catheti) constantly touch one 
another. The opposite — large side touching 
small — we have in Fig. 82, and by traveling 
from right to left of half the triangles, series 



GUIDE TO KINDER-GARTNERS. 



35 



G, 82 to 87, is produced. We would have 
produced a much larger number of forms, if 
we had not interrupted progress by turning 
the triangles produced by Fig. 86. 

In the fundamental forms 70 and 82, the 
sides touched one another. Fig. 88 shows 
that they may touch at the corners only. In 
this figure, the right angles are without ; in 
89 and 90, they are within. Fig. 90 is the 
mediation between 70 and 89, for four tablets 
touch with their sides (70) four with the cor- 
ners (89). No. 91 is the opposite of 90, full 
center, (empty center.) and mediation between 
88 and 89 — (four right angles without, as in 
88, and four within, as in 89.) It is already 
seen, from these indications, what a treasure 
of forms enfolds itself here, and how, with 

SIXTEEN TABLETS, 

it again will be multiplied. 

It would be impossible to exhaust them. 
Least of all, should it be the task of this 
work to do this, when it is only intended to 
show how the productive selfoccupation of 
the pupil can fittingly be assisted. We be- 
lieve, besides, that we have given a .suffi- 
cient number of ways on which fantasy may 
travel, perfectly sure of finding constantly 
new, beautiful, eye and taste developing for- 
mations. We, therefore, simply add the series 
J and K, the first of which is produced by 
quadrupling some of the elementary forms 
given at D, 48 to 59, and the second of which 
indicates how new series of forms of beauty 
may be developed from each of these forms. 
It must be evident, even to the casual ob- 
ser\-er, how here also the law of opposites, 
and their junction, was obsen^ed. Opposites 
are 92 and 93 ; mediation, 94 and 95 :' oppo- 
sites, 96 and 97 ; mediation, 98, 99, and 100: 
opposites, loi and 102 ; mediation, 103, etc. 

WITH THIRTY-TWO TABLETS. 

As heretofore, we proceed here also in the 
same manner, by multiplying the given ele- 
ments, or by means of further development, 
according to the law of opposites. As an 



example, we give Series L, the members of 
which are produced by a four-fold junction 
of the elements 68 and 69. no and iii are 
opposites; 112 and 113 mediative forms. 

WITH SIXTV-FOUR TABLETS. 

Here, also, the combined activity of many 
children will result in forms interesting to be 
looked at, not only by little children. There 
is another feature of this combined activity 
not to be forgotten. The children are busy 
obeying the same law ; the same aim unites 
them — one helps the other. Thus the condi- 
tions of human society — family, community, 
states, etc., — are already here shown in their 
effects. A system of education which, so to 
speak, by mere play, leads the child to appre- 
ciate those requisites, by compliance with 
which it can successfully occupy its position 
as man in the future, certainly deserves the 
epithet of a natural and rational one. 

Figures 114, 115, 116, are enlarged pro- 
ductions from 96 and 97. They are planned 
in such a way, as to admit of being continued 
in all directions, and thus serve to carry out 
the representation of a veiy large design. 

After having acted so far, according to in- 
dications made here, it is now advisable to 
start from the fundamental forms presented 
in the Fifth Gift, and to use them, with the 
necessary modifications, in forther occupying 
the pupils with the tablets. Fig. 117 gives 
a model, showing how the motives of the 
Fifth Gift can be used for this purpose. 

FORMS OF KNOWLEDGE. 

(plate XXII.) 

By joining two, four, and eight tablets, we 
have already become acquainted with the 
regular figures which may be formed with 
them, namely, triangle, quadrangle (square), 
right angle, rhomboid, and trapezium (Plate 
XXII., Figs. 1 18-123). 

The tablets are, however, especially quali- 
fied to bring to the observation of the child 
different sizes in equal forms (similar figures), 
and equal sizes in different forms. 



36 



GUIDE TO KINDER- GARTNERS. 



Figures 124, 125, and 126 show triangles 
of wliich each is the half of the following, 
and Nos. 129, 127, and 128, three squares 
of that kind. Figures 1 19-123, and 129- 
131, show the former five, the latter three 
times the same size in different forms. 

That the contemplation of these figures, 
the occupation with them, mu'st tend to facili- 
tate the understanding of geometrical axioms 
in future, who can doubt? And who can 
gainsay that mathematical instruction, by 
means of Froebel's method, must needs be 
facilitated, and better results obtained ? That 
such instruction, then, will be rendered more 
fruitful for practical life, is a fact which will 
be obvious to all, who simply glance at our 
figures, even without a thorough explanation. 
They contain demonstratively the larger num- 
ber of the axioms in elementary geometry, 
which relate to the conditions of the plane in 
regular figures. 

For the present purpose, it is sufficient if 
the child learns to distinguish the various kinds 
of angles, if it knows that the right angles 
are all equally large, the acute angles smaller, 
and the obtuse angles larger than a right 
angle, which the child will easily understand 
by putting one upon another. A deeper in- 
sight in the matter must be reserved for the 
primary department of instruction. 

C. THE EQUILATERAL TRIANGLE. 

(plates XXIV. AND X.XV.) 

So far the right angle has predominated in 
the occupations with the tablets, and the 
acute angle only appeared in subordinate 
relations. Now it is the latter alone which 
governs the actions of the child in producing 
forms and figures. 

The child will compare the equilateral 
triangle, which it receives in gifts of 3, 6, 9, 
and 12, first with the isosceles, right-angled 
tablet already known to him. Both have three 
sides, both three angles, but on close observa- 
tion not only their similarities, but also their 
dissimilarities will become apparent. The 
three angles of the new triangle are all smaller 



than a right angle, are acute angles and the 
three sides are just alike,- hence the name — 
equilateral — meaning "■ eqtcal sided" triangle. 

Joining two of these equilateral tablets the 
child will discover that it cannot form any 
of the regular figures previously produced. 
No triangle, no square, no right angle, no 
rhomboid, can be produced, but only a form 
similar to the latter, a rhomboid with four 
equal sides. To undertake to produce forms 
of life with these tablets would prove very 
unsatisfactory. Of particular interest, how- 
ever, because presenting entirely new forma- 
tions, are 

THE FORMS OF BEAUTY. 
The child first receives three tablets and 
will find the various positions of the same 
towards one another according to the law of 
opposites and their combination. Vide Plate 
XXIV., 1-9. 

SIX TABLETS. 

The child will unite his tablets around one 
common center (Fig. 10), form the opposite 
(Fig 11), and then arrive at the forms of me- 
diation 12, 13, 14, and 15, or it unites three 
elementary forms each composed of two tab- 
lets as done in 16, and forms the opposite 
17 and the mediations 18 and 19, or it starts 
from No. 10, turning first i, then 2, then 3 
tablets, outwardly. By turning one tablet, 
21 and 22, by turning two tablets, 23, 24, 25, 
26, 27, 28 and 29, are produced from No. 20. 
This may be continued with 3, 4, and 5 tab- 
lets. All forms thus received give us ele- 
mentary forms which may be employed as 
soon as a larger number of tablets are to be 
used. ^ 

NINE TABLETS. 

As with the right-angled triangle, small 
groups of tablets were combined to form 
larger figures, so we also do here. The ele- 
mentary forms under A give us in threefold 
combination the series of forms under C, 30 — 
40, which in course of the occupation may be 
multiplied at will. 



GUIDE TO KINDER-GARTNERS. 



37 



TWELVK TABLETS. 
(PLATE XXV.) 

Half of the tablets are painted brown, the 
balance l)lue By this difterence in color, op- 
positis are rendered more conspicuous, and 
these twelve tablets thus aftbrd a splendid 
opportunity for illustrating more forcibly the 
law of opposites and their combination. 
Plate XXV. shows how, by combination of 
opposites in the forms a and b, every time 
the star c is produced. Entirely new series of 
forms may be produced by employing a larger 
number of tablets, i8, 24 or 36. We are, 
however, obliged to leave these representa- 
tions to the combined inventive powers of 
• teacher and pupil. 

FORMS OK RXOWl.EDGE. 

It has been mentioned before, that the 
previously introduced regular mathematical 
tlgures do not appear here as a whole. How- 
ever, a triangle can be represented by four or 
nine tablets, a rhomboid by four, six or eight 
tablets, a trapezium l)y three, and manifold 
instructive remarks can be made and experi- 
ences gathered in the construction of these 
figures. But above all, it is the rhombus 
and hexagon, with which the pupil is to be 
made acquainted here. The child unites two 
triangles by joining side to side, and thus 
produces a rhombus. 

The child compares the sides — are they 
alike ? What is their direction ? Are they 
parallel ? Two and two have the same di- 
rection, and are therefore parallel. 

The child now examines the angles and 
finds that two and two are of equal size. 
'I'hey are not right angles. Triangles, smaller 
than right angles, he knows, are called acute 
angles, and he hears now that the larger 
ones are called olMuse angles. The teacher 
may remark that the latter are twice the size 
of the former ones. By these remarks the 
pupil will gradually receive a correct idea of 
the rlionibus and of the qualities by which it 
is distinguished from the quadrangle, right 
angle, trapezium and rhomboid. 
6 



In the same manner, the hexagon gives 
occasion for interesting and instructive ques- 
tions and answers. How many sides has it ? 
How many are parallel ? How many angles 
does it contain ? What kind of angles are 
the)- ? How large are they as compared with 
the angles of the equal sided triangle.' Twice 
as large. 

The power of observation and the reason- 
ing faculties are constantly developed by such 
conversation, and the results of such exer- 
cises are of more importance than all the 
knowledge that may be acquired in the mean- 
time. 

The greater part of this occupation, how- 
ever, is not within the Kinder-Garten proper, 
but belongs to the realm of the Primary' 
School Department. If thej' are introduced 
in the former, they are intended only to swell 
the sum of general experience in regard to 
the qualities of things, whereas in the latter, 
they serve as a foundation for real knowledge 
in the department of mathematics. 

D. THE OBTUSE-ANGLED TRIANGLE WITH 

TWO SIDE.S ALIKE. 

(plates xxvl and xxvil) 

The child receives a box with sixty-four 
obtuse-angled tablets. It examines one of 
them and compares it with the right-angled 
triangle, with two sides alike. It has two 
sides alike, has also two acute angles, but the 
third angle is larger than the right angle ; it 
is an obtuse angle, and the tablet is, there- 
fore, an obtuse-angled triangle with two sides 
alike. 

The pupil then unites two and two tablets 
by joining their sides, corners, sides and 
corners, and vice versa, as shown in Figs. 1-8, 
on Plate XXVI. 

The next preliminary exercise, is the com- 
bination, by fours, of elementary forms thus 
produced. Peculiarly beautiful, mosaic-like 
forms of beauty result from this process. 
The Pigs. 9-15 aftbrd examples which were 
produced by combination of two opposites, 
a and b, or by mediative forms c and d. In 



38 



GUIDE TO KINDER-GARTNERS. 



Figs. 16-22 we have finally some few sam- 
ples of forms of life. 

The forms of knowledge which may be 
produced, afford opportunity to repeat what 
has been taught and learned previously about 
proportion of form and size. In the Primary 
School the geometrical proportions are further 
introduced, by which irjeans the knowledge 
of the pupils, in regard to angles, as to the 
position they occupy in the triangle, can be 
successfully developed by practical observa- 
tion, without the necessity of ever dealing in 
mere abstractions. 

E. THE RIGHT-ANGLED TRIANGLE WITH 
NO EQUAL SIDES. 

(PLATES XXVIII. AND XXIX.) 

The little box with fifty-six tablets of the 
above description, each of which is half the 
size of the obtuse-angled triangle, enables the 
child to represent a goodly number of forms 
of life, as shown on Plate XXIX. 

In producing them, sufficient opportunities 
will present themselves, to let the child find out 
the qualities of the new occupation material. 

A comparison with the right angled triangle 
with two equal sides will facilitate the matter 
greatly. 

On the whole, howe^■er, the process of de- 
velopment may be pursued, as repeatedly in- 
dicated on previous occasions. 



The variety of the forms of beaut)' to be laid 
with these tablets, is especially founded on 
their combination in twos. Plate XXVIII., 
Figs. 1-6, shows the forms produced by join- 
ing equal sides. 

In similar manner, the child has to find out 
the forms which will be the result of joining 
unlike sides, like corners, unlike corners, and 
finally, corners and sides. 

By a fourfold combination of such element- 
ary forms the child receives the material, 
(Figs. 7-18,) to produce a large number of 
forms of beauty similar to those given under 
19-22. 

For the purpose, also, of presenting to the 
child's observation, in a new shape, propor- 
tions of form and size, in the production of 
forms of knowledge, these tablets are very 
serviceable. 

Like the previous tablets, these also, and a 
following set of similar tablets, are used in 
the Primary Department for enlivening the 
instruction in Geometry. It is believed that 
nothing has ever been invented to so facilitate, 
and render interesting to teacher and pupil, 
the instruction in this so important branch of 
education as the tablets forming the Seventh 
Gift of Froebel's Occupation Material, the use 
of which is commenced with the children when 
they have entered the second year of their 
Kinder-Garten discipline. 



THE EIGHTH GIFT. 



STAFFS FOR LAYING OF FIGURES. 



(PLATES XXX. TO XXXIII.) 



As the tablets of the Seventh Gift are 
nothing but an embodiment of the planes sur- 
rounding or limiting the cube, and as these 
planes, limits of the cube, are nothing but 
the representations of the extension in length, 
breadth, and height, already contained in the 
sphere and ball, so also the staffs are derived 
from the cube, forming as they do, and here 
bodily representing its edges. But they are 
also contained in the tablets, because the 
plane is thought of, as consisting of a con- 
tinued or repeated line, and this may be 
illustrated by placing a sufficient number of 
one inch long staffs side by side, and close 
together, until a square is formed 

The staffs lead us another step farther, 
from the material, bodily, toward the realm 
of abstractions. 

By means of the tablets, we were enabled 
to produce flat images of bodies ; the slats, 
which, as previously mentioned, form a tran- 
sition from plane to line, gave, it is true, the 
outlines of forms, but these outlines still re- 
tained a certain degree of the plane about 
them ; in the staffs, however, we obtain the 
material to draw the outlines of objects, by 
bodily lines, as perfectly as it can possibly 
be done. 

The laying of staffs is a favorite occupa- 
tion with all children. Their fantasy sees in 
them the most different objects, — stick, yard 
measure, candle ; in short, they are to them 
representatives of every thing straight. 

Our staffs are of the thickness of a line 
(one twelfth of an inch), and are cut in vari- 
7 



ous lengths. The child, holding the staff in 
hand, is asked : What do you hold in your 
hand.? How do you hold it? Perpendicu- 
larly. Can you hold it in any other way.' 
Yes ! I can hold it horizontally. Still in 
another way? Slanting from left above, to 
right below, or from right above to left 
below. 

Lay your staff upon the table. How does 
it lie ? In what other direction can you place 
it? (Plate XXX. A.) 

The child receives a second staff. How 
many staffs have you now ? Now try to form 
something. The child lays a standing cross, 
(Fig. 4.) You certainly can lay many other 
and more beautiful things ; but let us see 
what else we may produce of this cross, by 
moving the horizontal staff, by half its lengfth, 
(Fig. B. 4 to 14.) Starting from a lying cross, 
(C. 15 — 23) or from a pair of open tongs, 
(where two acute and two obtuse angles are 
formed by the crossing staffs,) and proceeding 
similarly as w-ith B, we will produce all posi- 
tions which two staffs can occupy, relative to 
one another, except the parallel, and this will 
give ample opportunit}- to refresh, and more 
deeply impress upon the pupil's mind, all that 
has been introduced so far, concerning per- 
pendicular, horizontal, and oblique lines, and 
of right, acute and obtuse angles. With two 
staffs, we can also form little figures, which 
show some slight resemblance with things 
around us. By them we enliven the power of 
recollection and imagination of the child, ex- 
ercise his abilit}' of comparison, increase his 



40 



GUIDE TO KINDER-GARTNERS. 



treasure of ideas, and develop, in all these 
his power of perception and conception — the 
most indispensable requisites for disciplining 
the mind. 

Our plates give representations of the fol- 
lowing objects : 

WITH TWO STAFFS. 
Fig. 24. A Playing Table. 
Fig. 25. A Weather-vane. 
Fig. 26. A Pickax. 

Fig. 27. An Angle measure. (Carpenter's 
square.) 

Fig. 28. A Candle stick. 
Fig. 29. Two Candles. 
Fig. 30. Rails. 
Fig. 31. Roof 

WITH THREE STAFFS. 
Fig. 32 A Kitchen Table. 
Fig. 33. A Garden Rake. 



Fig. 34 


A Flail. 


WITH SEVEN STAFFS. 


Fig. 35- 


An Umbrella. 


Fig. 74. A Window. 


Fig. 36. 


A Hay Fork. 


Fig. 75. A Stretcher. 


Fig. 37- 


A Small Flag. 


Fig. 76. A Dwelling-house. 


Fig. 38. 


A Steamer. 


Fig. 77. Steeple with Lightning-rod. 


Fig. 39- 


A Whorl. 


Fig. 78. A Balance. 


Fig. 40. 


A Star. 


Fig. 79. Piano-forte. 

Fig. 80. A Bridge with Three Spans 




WITH FOUR STAFFS. 


Fig. 81. An Inn Sign. 


Fig. 41- 


A Small Looking-glass. 


Fig. 82. Crucifix and Two Candles. 


Fig. 42. 


A Wooden Chair. 


Fig. 83. Tombstone and Cross. 


Fig. 43- 


A Wash-bench. 


Fig. 84. Rail Fence. 


Fig. 44- 


Kitchen Table with Candle. 


Fig. 85. Garret Window. 


Fig. 45- 


A Crib. 


Fig. 86. Flower Spade. 


Fig. 46. 


A Kennel. 


Fig. 87. A Star Flower. 


Fig. 47- 


Sugar-loaf. 




Fig. 48. 


Flower pot. 


WITH EIGHT STAFFS. 


Fig. 49- 


. Signal-post. 


Fig. 88. Book-shelves. 


Fig. 5°- 


Flower-stand. 


Fig. 89. Church, with Steeple. 


Fig. 51- 


Crucifix. 


Fig. 90. Tombstone and Cross. 


Fig 52- 


A Grate. 


Fig. 91. Gas Lantern. 
Fig. 92. Windmill. 




WITH FIVE STAFFS. 


Fig. 93. A Tower. 


Fig. S3- 


Signal Flag of R. R. Guard. 


Fig. 94. An Umbrella. 


Fig. 54. 


Chest of Drawers. 


Fig. 95. A Carrot. 


Fig- 55- 


A Cottage. 


Fig. 96. A Flower-pot. 



Fig. 56 


A Steeple. 


Fig. 57- 


A Funnel. 


Fig. 58. 


A Beer Bottle. 


Fig. 59. 


A Bath Tub. 


Fig. 60. 


A (broken) Plate. 


Fig. 61. 


A Roof 


Fig. 62. 


A Hat. 


Fig. 63. 


A Chair. 


Fig. 64. 


A Lamp Shade. 


Fig. 65. 


A Wine-glass. 


Fig. 66. 


A Grate. 



WITH SIX STAFFS. 
Fig. 67. A Large Frame. 
Fig. 68. A Flag. 
Fig. 69. A Barn. 
Fig. 70. A Boat. 
Fig. 71. A Reel. 
Fig. 72. A Small Tree. 
Fig 73. A Round Table. 



GUIDE TO KINDER-GARTNERS. 



Fig. 97. A large Wash tub. 
Fig. 98. A large Rail Fence. 
Fig. 99. A large Kitchen Table. 
Fig 100. A Shoe. 
Fig. 1 01. A Butterfly. 
Fig. 102. A Kite. 

WITH NINE STAFFS. 

Fig. 103. Church with Two Steeples. 

Fig. 104. Dwelling-house. 

Fig. 105. Coffee-mill. 

Fig. 106. Kitchen Lamp. 

Fig. io7. Sail-boat. 

Fig. loS. Balance. 





WITH TEN STAFFS. 


Fig. 


109. A Tower. 


Fig. 


no. A Drum. 


Fig. 


III. Grave-yard Wall. 


Fig. 


112. A Hall. 


Fig. 


113. A Flowerpot. 


Fig. 


114. A Street Lamp. 


Fig. 


115. A Satchel. 


Fig. 


116. A Double Frame. 


Fig. 


117. A Bedstead. 


Fig. 


118. A row of Barns. 


Fig. 


119. A Flag. 




WITH ELEVEN STAFFS. 


Fig. 


1 20. A Kitchen Lamp. 


Fig. 


121. A Pigeon-house. 


Fig. 


122. A Farm-house. 


Fig. 


123. A Sail-boat. 


Fig. 


124. A Student's Lamp. 




WITH TWELVE STAFFS. 


Fig. 


125. A Church. 


Fig. 


126. A Window. 


Fig. 


127. Chair and Table. 


Fig. 


128. A Well with Sweep. 



These exercises are to be continued with a 
larger number of staffs. The hints given 
above, will enable the teacher to conduct the 
laying of staffs in a manner interesting, as well 
as useful, for her pupils. 

It is advisable to guide the activity of the 



child occasionally in another direction. The 
pupils may all be called upon to lay tables, 
which can be produced from two to ten staffs, or 
houses which can be laid with eighteen staffs. 

Another change in this occupation can be 
introduced by employing two, four, or eight 
times, divided staffs. It is obvious that, in 
this manner, the figures may often assume a 
greater similarity and better proportions than 
is possible if only staffs of the same length are 
employed. 

If a staff is not entirely broken through, 
but only bent with a break on one side, an 
angle is produced. If a staff forms several 
such angles, it can be used to represent a 
curved or rounded line, and by so doing a new 
feature is introduced to the class. 

Staffs are also employed for representing 
forms of beauty. The previous, or simulta- 
neous occupation with the building blocks, 
and tablets, will assist the child in producing 
the same in great variety. Figures 121 — 124 
on Plate XXXIII. belong to this class of repre- 
'sentations. 

Combination of the occupation material of 
several, or all children taking part in the ex- 
ercises, will lead to the production of larger 
forms of life, or beauty, which in the Primary 
Department, can even be extended to repre- 
senting whole landscapes, in which the mate- 
rial is augmented by the introduction of saw- 
dust to represent foliage, grass, land, moss, 
etc. Plate XXXIII. gives, un(3er Fig. 120, a 
specimen of such a production-^-on a very re- 
duced scale. 

By means of combination, the children 
often produce forms which afford them great 
pleasure, and repay them for the careful per- 
severance and skill employed. .They often 
express the wish that they might be able to 
show the production to father, or mother, or 
sister, or friend. But this they cannot do, as 
the staffs will separate when taken up. 

We should assist the little ones in carrying 
out their desire, of giving pleasure to others, 
by showing to, or presenting them with the 
result of their own industry, in portable form. 



42 



GUIDE TO KINDER-GARTNERS. 



By wetting the ends of the staffs with mucil- 
age, or binding them together with needle 
and thread, or placing them on substantial 
paper, we can grant their desire, and make 
them happy, and be sure of their thanks for 
our efforts. 

We employ the same means of rendering 
permanent the production of staff-laying in 
our instruction in reading, where letters are 
fastened to paper by mucilage, thus impress- 
ing upon the child's mind more lastingly, the 
visible signs of the sounds he has learned. 

But we have still another means of render- 
ing these representations permanent, and it is 
by drawing, which, on its own account, is to 
be practiced in the most elementary manner. 
We begin the drawing, as will hereafter be 
shown, as a special branch of occupation, as 
soon as the child has reached its third or 
fourth year. 

The child is provided with a slate, upon 
whose surface, a net-work of horizontal and 
perpendicular lines is drawn. Instead of lay- 
ing the staff upon the table, the child places 
it upon the slate. Taking the staff from its 
place, he draws with the slate pencil, in its 
stead, a line as long as the staff, in the same 
direction. He draws the perpendicular staff. 
The horizontal, slantingly laid staff, is drawn 
in all its variations in like manner, perpendic- 
ular, and horizontal ; perpendicular and ob- 
lique, or horizontal and oblique staffs are 
brought in contact with one another, and 
these connections reproduced by drawing. 

The method of laying staffs is in general 
the same, applied for drawing, the latter, how- 
ever, progresses less rapidly. It is advisable 
to combine staffs in regular figures, triangles 
and squares, and to find out in a small num- 
ber of such figures all possible combinations 
according to the law of opposites. Plates 
XXIV. and XXV. will furnish material for this 
purpose. 

All these occupations depend on the larger 
or smaller number of staffs employed ; they 
therefore afford means for increasing and 
strengthening the knowledge of the child. 



The pupil, however, is much more decidedly 
introduced into the elements of ciphering, 
when the staffs are placed into his hands for 
this specific purpose. We do not hesitate to 
make the assertion that there is no material 
better fitted to teach the rudiments in figures, 
as also the more advanced steps in arithme- 
tic, than Froebel's staffs, and that by their in- 
troduction, all other material is rendered use- 
less. A few packages of the staffs in the 
hands of the pupil is all that is needed in the 
Kinder Garten proper, and the following De- 
partment of the Primary. 

The children receive a package with ten 
staffs each. Take one staff and lay it per- 
pendicularly on the table. Lay another at 
the side of it. How many staffs are now be- 
fore you ? Twice one makes two. 

Lay still another staff upon the table. 
How many are there now? One and one 
and one — two and one are three. 

Still another, etc., etc., until all ten staffs 
are placed in a similar manner upon the 
table. Now take away one staff. How many 
remain ? Ten less one leaves nine. Take 
away another staff from these nine. How 
many are left.' Nine less one leaves eight 

Take another; this leaves ? seven, etc., 

etc., until all the staffs are taken one by one 
from the table, and are in the child's hand 
again. Take two staffs and lay them upon 
the table, and place two others at some dis- 
tance from them. (|| ||) How many are now 
on the table ? Two and two are four. Lay 
two more staffs beside these four staffs. How 
many are there now ? Four and two are six. 
Two more. How many are there now ? Six 
and two are eight. And still another two. 
How many now ? Eight and two are ten. 

The child has learned to add staffs by twos. 
If we do the opposite, he will also learn to 
subtract by twos. In similar manner we pro- 
ceed with three, four, and_;?z.'^. After that, we 
alternate, with addition and subtraction For 
instance, we lay three times two staffs upon the 
table and take away twice two, adding again 
four times two. Finally we give up the 



GUIDE TO KINDER- GARTNERS. 



43 



equality of the number and alternate, by ad- 
ding different numbers. We lay upon the 
table 2 and 3 staffs=5, adding 2=7 adding 
3=10. This affords opportunity to intro- 
duce 6 and 9, as a whole, more frequently 
than was the case in previous exercises. In 
subtraction we observe the same method, and 
introduce exercises in which subtraction and 
addition alternate with unequal numbers. 
Lay 6 staffs upon the table, take 2 away, add 
4, take away i, add 3, and ask the child how 
many staffs are on the table, after each of 
these operations. 

In like manner, as the child learned the 
figures from one to ten, and added and sub- 
tracted with them as far as the number of 10 
staffs admitted, it will now learn to use the 
lo's up to 100. Packages of 10 staffs are 
distributed. It treats each package as it did 
before the single staff. One is laid upon the 
table, and the child says, "Once ten ;" add a 
second, " Twice ten ; " a third, " Three times 
ten," etc. Subsequently it is told, that it is 
not customary to say twice, or two times ten, 
but twenty; not three times ten, but thirty, 
etc. This experience will take root so much 
the sooner, in his memory, and become 
knowledge, as all this is the result of his own 
activity. 

As soon as the child has acquired sufficient 
ability in adding and subtracting by tens, the 
combination of units and tens is introduced. 

The pupil receives two packages of ten 
staffs — places one of them upon the table, 
opens the second and adds its staffs one by 
one to the ten contained in the whole pack- 
age. He learns 10 and i = ii, 10 and 2=12, 
10 and 3 = 13, until 10 and 10 = 20 staffs. 
Gathering the 10 loose staffs, the child re- 
ceives another package and places it beside 
the first whole package. 10 and 10=20 
staffs. Then he adds one of the loose staffs, 
and says 20 and 1=21,20 and 2 = 22, etc. 
Another package of 10 brings the number to 
31, etc., etc., up to 91 staffs. In this manner 
he learns 22, 32, up to 92, 23 to 93, and 100, 
and to add and subtract within this limit. 



To be taught addition and subtraction in 
this manner, is to acquire sound knowledge, 
founded on self-activity and experience, and 
is far superior to any kind of mind-killing 
memorizing usually employed in this connec- 
tion. 

If addition and subtraction are each other's 
opposites, so addition and multiplication on 
the one hand, and subtraction and division 
on the other, are oppositionally equal, or, 
rather, multiplication and division are short- 
ened addition and subtraction. 

In addition, when using equal numbers of 
staffs, the child finds that by adding 2 and 2 
and 2 and 2 staffs it receives 8 staffs, and is 
told that this may also be expressed by saying 
4 times 2 staffs are 8 staffs. It will be easy 
to see how to proceed with division, after the 
hints given above. 

It has been previously mentioned that for 
the representation of forms of life and beauty, 
the staffs frequently need to be broken. This 
provides material for teaching fractions, in the 
meantime. The child learns by observtion 
i staff, i, -J, i, etc. The proportion of the 
part or of several equal parts to the whole, 
becomes clear to him, and finally it learns to 
add and subtract equal fractions, in element- 
ary form, in the same rational manner. 

Let none of our readers misunderstand us 
as intimating that all this should be accom- 
plished in the Kinder-Garten proper. 

Enough has been accomplished if the child 
in the Kinder Garten, by means of staffs and 
other material of occupation, has been en- 
abled to have a clear understanding of figures 
in general. 

This will be the basis for further develop- 
ment in addition, subtraction, multiplication 
and division in the Primaiy Department. 

It now remains to add the necessary advice 
in regard to the introduction and representa- 
tion with staffs of the nuvierah. In order to 
make the children understand what nnmerals 
are, use the blackboard and show them that 
if we wish to mark down how many staffs, 
blocks, or other things each of the children 



44 ■ 



GUIDE TO KINDER-GARTNERS. 



have, we might make one Hne for each staff, 
block, etc. Write then one small perpendicu- 
lar line on the blackboard, saying in writing, 
Charles has one staff; making hiw lines below 
the first, continue by saying, Emma has two 
blocks; again, making three lines, Ernest has 
three rubber balls, and so on until you have 
written ten lines, always giving the name of 
the child and stating how many objects it has. 
Then write opposite each row of lines to the 
right, the Arabic figure expressing the number 
of lines, and remark that instead of using so 
many lines, we can also use these figures, 
which we call numerals. Then represent with 
the little staff these Arabic figures, some of 
which require the bending of some of the 
staffs, on account of the curved lines. 

After the children have learned that the 
figures which we use for marking down the 
number of things are called numerals, exer- 
cises of the following character may be intro- 
duced : 

How many hands has each of you .' Two. 
The numeral 2 is written on the board. How 
many fingers on each hand ? Five. This is 
written also on the board — 5. How many 
walls has this room ? Four. Write this figure 
also on the board. How many days in the 
week are the children in the Kinder-Garten ? 
Six days. The 6 is also written on the board. 

Then repeat, and let the children repeat 
after you, as an exercise in speaking, and at 
the same time, for the purpose of recollecting 
the numerals : 

Each child has 2 hands, on each hand are 
5 fingers ; this room has 4 walls, — always 
emphasizing the numerals, and pointing to 
them when they are named. 

The children may then count the objects in 
the room, or elsewhere, and then lay, with 
their staffs, the numerals expressing the num- 
ber they have found, speaking in tlie mean- 
time, a sentence asserting the fact which they 
have stated. 

After having introduced the numerals in 
this manner, the teacher, on some following 
day, may proceed to reading exercises. 



The second part of this Guide contains 
systematically arranged material for instruc- 
tion in reading, according to the phonetic 
method. 

Suffice it to say, tliat it is begun in the 
same manner in which numerals were intro- 
duced. As by means of numerals, I could 
mark on the blackboard the number of things, 
so I can also mark on the board the names of 
things, their qualities and actions. In doing 
this I write words, and zcords consist of let 
ters. Besides the words expressing names of 
things, their qualities and actions, which are 
the most important words in every language, 
there are other words which are used for 
other purposes. Such words are, for example, 
no, now, never. Should I ask you, is any one 
of you asleep, what would you answer ? " No, 
sir. We are all awake." I will write the lit- 
tle word " no," on the blackboard, because it 
is the most important word in your answer. 
There it stands, " no." And now I will ask you : 
"Have you ever been in a Kinder-Garten?" 
" Yes, sir, we are now in a Kinder-Garten 
school." I will write on the board the little 
wox^," now." There it stands, " w^w ;" and 
another question I will now ask you : " Should 
we ever kill an animal for the mere pleasure 
of hurting it ? " " No, sir, «67rr." I will also 
write the word " nex'er" on the board. There 
it is, '■'■never." I will now pronounce these 
three words for you, and each of you will 
repeat them in the same manner in which I 
do. N o! N ow! N ever! Chil- 
dren, in repeating, always dwell on the n 
sound longer than on any other part of the 
word. They are then led to observe the 
similarity of sound in pronouncing the three 
words, then to observe the similarity of the 
first letter in all of them, and finally the dis- 
similarity of the remaining part of the words 
in sound, and its representations — the letters. 

I will now take away these words from 
the blackboard, and write something else upon 
it. I again write the " n" and the children 
will soon recognize it as the letter previously 
shown. 



GUIDE TO KINDER-GARTNERS. 



45 



For the continuation of instruction in read- 
ing, we refer tlie reader to the second part of 
the " Guide," where all necessary information 
on this important branch of instruction will 
be found. 

As the occupation with laying staffs, is one 



of the earliest in the Kinder Garten, and is em- 
ployed in teaching numerals, and reading and 
writing, and drawing also, it is evident how 
important a material of occupation was sup- 
plied by Froebel, in introducing the staffs as 
one of his Kinder-Garten Gifts. 



THE NINTH GIFT. 



WHOLE AND HALF RINGS FOR LAYING FIGURES. 



Immediately connected with the staffs, or 
straight lines, Froebel gives the representa- 
tives of the rounded, curved lines, in a box 
containing twenty-four whole and fort}'-eight 
half circles of two different sizes made of 
wire. We have heretofore introduced the 
curved line by bending the staff; this, how- 
ever, was a rather imperfect representation. 
The rings now introduced supply the means 
of representing a curved line perfectly, be- 
sides enabling us by their different sizes to 
show " the one within another " more plainly 
than it could be done with the staffs, as the 
above, upon, below, aside of each other, etc., could 
well be represented, but not the " within " in 
a perfectly clear manner. 

This Gift is introduced in the same way as 
all other previous Gifts were introduced, and 
the rules by which this occupation is carried 
on must be clear to every one who has fol- 
lowed us in our " Guide " to this point. 

The child receives one whole ring and two 
half rings of the larger size. Looking at the 
whole ring the children obser\'e that there is 
neither beginning nor end in the ring — that it 
represents the circle, in which there is neither 
beginning nor end. With the half ring, they 
have two ends ; half rings, like half circles 
and all other parts of the circle or curved 
lines, have two ends. Two of the half rings 



form one whole ring or circle, and the chil- 
dren are asked to show this by experiment, 
(Fig. I, Plate XXXIV). Various observations 
can be made by the children, accompanied by 
remarks on the part of the teacher. When- 
ever the child combined two cubes, two tablets, 
staffs or slats with one another, in all cases 
where corners and angles and ends were con- 
cerned in this combination, corners and angles 
were again produced. The two half rings or 
half circles, however, do not form any angles. 
Neither could closed space be produced by 
two bodies, planes, nor lines ! — the two half 
circles, however, close tightly up to each 
other, so that no opening remains. 

The child now places the two half circles 
in opposite directions, (Fig. 2.) Before the 
ends touched one another, now the middle of 
the half circles ; previously a closed space 
was formed, now both half circles are open, 
and where they touch one another, angles 
appear. 

Mediation is formed in Fig. 3, where both 
half circles touch each other at one end and 
remain open, or, as indicated by the dotted 
line, join at end and middle, thereby enclosing 
a small plane and forming angles in the mean- 
time. 

Two more half circles are presented. The 
child forms Fig. 4, and develops by moving 



46 



GUIDE TO KINDER-GARTNERS. 



the half circles in the direction from without, 
to within Fig 5, 6, 7, and 8. 

The number of circles is increased. Fig. 
9, 10, and II show some forms built of 8 half 
circles. 

All these forms are, owing to the nature of 
the circular line, forms of beauty, or beauti- 
ful forms of life, and, therefore, the occupa- 
tion with these rings, is of such importance. 
The child produces forms of beauty with 
other material, it is true, but the curved line 
suggests to him in a higher degree than any- 
thing else, ideas of the beautiful, and the 
simplest combinations of a small number of 
half and whole circles, also bear in themselves 
the stamps of beauty. 

If the fact cannot be refuted, that merely 
looking at the beautiful, favorably impresses 
the mind of the grown person, in regard to 
direction of its development, enabling him to 
more fully appreciate the good, and true, and 
noble, and sublime, this influence, upon the 
tender and pliable soul of the child, must 
needs be greater, and more lasting. Without 
believing in the doctrine of two inimical 
natures in man, said to be in constant con- 
flict with each other, we do believe that the 



talents and disposition in human nature are 
subject to the possibility of being developed 
in two opposite directions. It is this possi- 
bility, which conditions the necessity of edu- 
cation, the necessity of employing every 
means to give the dormant inclinations and 
tastes in the child, a direction toward the 
true, and good, and beautiful, — in one word, 
toward the ideal. Among these means, stands 
pre-eminently a rational and timely develop- 
ment of the sense of beauty, upon which 
Froebel lays so much stress. 

Showing the young child objects of art which 
are far beyond the sphere of its appreciation 
however, will assist this development, much 
less than to carefully guard that its surround 
ings contain, and show the fundamental req 
uisites of beauty, viz. : order, cleanliness, sim 
plicity, and harmony of form, and giving as^ 
sistance to the child in the active representa 
tion to the beautiful in a manner adapted to 
the state of development in the child himself. 

Like forms laid with staffs, those repre 
sented with rings and half rings also, are 
imitated by the children by drawing them on 
slate or paper. 



THE TENTH GIFT. 



THE MATERIAL FOR DRAWING. 



(PLATES XXXV. TO 



•) - 



One of the earliest occupations of the child 
should be methodical drawing. Froebel's 
opinion and conviction on this subject, de- 
viates from those of other educators, as much 
as in other respects. Froebel, however, does 
not advocate drawing, as it is usually prac- 
ticed, which on the whole, is nothing else but 
a more or less thoughtless mechanical copy- 



ing. The method advanced by Froebel, is in- 
vented by him, and perfected in accordance 
with his general educational principles. 

The pedagogical effect of the customary 
method of instruction in drawing, rests in 
many cases simply in the amount of trouble 
caused the pupil in surmounting technical 
difficulties. Just for that reason it should be 



GUIDE TO KIXDER-GARTNERS. 



47 



abandoned entirely for the youngest pupils, 
for the difficukics in many cases are too great 
for the child to cope with. It is a work of 
Sisyphus, labor without result, naturally tend- 
ing to extirpate the pleasure of the child in its 
occupation, and the unavoidable consequence 
is that the majority of people will never reach 
the point where they can enjoy the fruits of 
their endeavors. 

If we acknowledge that Froebel's educa- 
tional principles are correct, namely, that all 
manifestations of the child's life are manifes- 
tations of an innate instinctive desire for 
development, and therefore should be fos. 
tered and developed by a rational education, 
in accordance with the laws of nature. Draw- 
ing should be commenced with the third year; 
nay, its preparatory principles should be intro- 
duced at a still earlier period. 

With all the gifts, hitherto introduced, the 
children were able to study and represent 
forms and figures. Thus they have been 
occupied, as it were, in drawing with bodies. 
This developed their fantasy, and taste, giving 
them in the meantime correct ideas of the 
solid, plane, and the embodied line. 

A desire soon awakes in the child, to rep- 
resent by drawing these lines and planes, 
these forms and objects. He is desirous of 
representation when he requests the mother 
to tell him a story, explain a picture. He is 
occupied in representation when breathing 
against the window-pane, and scrawling on it 
with its finger, or when trying to make figures 
in the sand with a little stick. Each child is 
delighted to show what it can make, and 
should be assisted in every way to regulate 
this desire. 

Drawing not only develops the power of 
representing things the mind has perceived, 
but affords the best means for testing how far 
they have been perceived correctly. 

It was Froebel's task to invent a method 
adapted to the tender age of the child, and 
its slight dexterity of hand, and in the mean- 
time to satisfy the claim of all his occupa- 
tions, i. €., that the child should not simply 



imitate, but proceed, self-actingly, to perform 
work which enables him to reflect, reason, 
and finally to invent himself. 

Both claims have been most ingeniously 
satisfied by Froebel. He gives the three 
years' old child a slate, one side of w^hich is 
covered by a net-work of engraved lines (one- 
fourth of an inch apart), and he gives him in 
addition, thereto, the law of opposites and 
their mediation as a rule for h's activity. 

The lines of the net-work guide the child in 
moving the pencil, they assist it in measuring 
and comparing situation and position, size 
and relative center, and sides of objects. 
This facilitates the work greatly, and in con- 
sequence of this important assistance the 
childs' desire for work is materially increased ; 
whereas, obstacles in the earliest attempts at 
all kinds of work must necessarily discourage 
the beginner. 

Drawing on the slate, with slate pencil is 
followed by drawing on paper with lead 
pencil. The paper of the drawing books is 
ruled like the slates. It is advisable to begin 
and continue the exercises in drawing on 
paper, in like manner as those on the slate 
were begun and continued, with this differ- 
ence only, that owing to the progress made 
and skill obtained by the child, less repeti- 
tions may be needed to bring the pupil to 
perfection here, as was necessary in the use 
of the slate. 

It has been repeatedly suggested, that 
whenever a new material for occupation is 
introduced, the teacher should comment upon, 
or enter into conversation with the children, 
about the same ; the difference between draw- 
ing on the slate and on paper, and the mate- 
rial used for both may give rise to many 
remarks and instructive conversation. 

It may be mentioned that the slate is first 
used, because the children can easily correct 
mistakes by wiping out what they have made, 
and that they should be much more careful in 
drawing on paper, as their productions can 
not appear perfectly clean and neat if it 
should be necessary to use the rublier often. 



48 



GUIDE TO KINDER- GARTNERS. 



Slate and slate pencil are of the same mate- 
rial ; paper and lead pencil are two very differ- 
ent things. On the slate the lines and figures 
drawn, appear white on darker ground. On 
the paper, lines and figures appear black on 
white ground. 

More advanced pupils use colored lead 
pencils instead of the common black lead 
pencils. This adds greatly to the appear- 
ance of the figures, and also enables the child 
to combine colors tastefully and fittingly. For 
the development of their sense of color, and 
of taste, these colored mosaic like figures are 
excellent practice. 

Drawing, as such, requires observation, at- 
tention, conception of the whole and its parts, 
the recollection of all, power of invention and 
combination of thought. Thus, by it, mind 
and fantasy are enriched with clear ideas and 
true and beautiful pictures. For a free and 
active development of the senses, especially 
eye and feeling, drawing can be made of in- 
calculable benefit to the child, when its natu- 
ral instinct for it is correctly guided at its 
very awakening. 

Our Plates XXXV. to XLVI. show the sys- 
tematic course pursued in the drawing depart- 
ment of the Kinder-Garten. The child is first 
occupied by 

THE PERPENDICULAR LINE. 

(PLATES XXXV. TO XXXVIII.) 

The teacher draws on the slate a perpen- 
dicular line of a single length (^ of an inch), 
saying while so doing, I draw a line of a single 
length downward. She then (leaving the line 
on the slate, or wiping it out) requires the 
child to do the same. She should show that 
the line she made commenced exactly at the 
crossing point of two lines of the net-work, 
and also ended at such a point. 

Care should be exercised that the child 
hold the pencil properly, not press too much 
or too little on the slate, that the lines drawn 
be as equally heavy as possible, and that each 
single line be produced by one single stroke 
of the pencil. The teacher should occasion- 



ally ask : What are you doing ? or, what have 
you done? and the child should always an- 
swer in a complete sentence, showing that it 
works understandingly. Soon the lines may 
be drawn upwards also, and then they may 
be made alternately up and down over the 
entire slate, until the child has acquired a cer- 
tain degree of ability in handling the pencil. 

The child is then required to draw a per- 
pendicular line of two lengths, and advances 
slowly to lines of three, four and five lengths, 
(Plate XXXV., Figs. 2—5). 

With the number five Froebel stops on 
this step. One to five are sufficiently known, 
even to the child three years old, by the 
number of his fingers. 

The productions thus far accompHshed are 
now combined. The child draws, side by 
side of one another, lines of one and two 
lengths (Fig. 6), of one, two and three lengths 
(Fig. 7), of one, two, three and four lengths 
(Fig. 8), and finally lines of one, two, three, 
four and five lengths (Fig. 9.) It always forms 
by so doing a right-angled triangle. We 
have noticed already, in using the tablets, that 
right-angled triangles can lie in many different 
ways. The triangle (Fig. 9 and 10) can also 
assume various positions. In Fig. 10 the 
five lines stand on the baseline — the smallest 
is the first, the largest the last, the right an- 
gle is to the right below. In Fig. 1 1 the op- 
posite is found — the five lines hang on the 
base-line, the largest comes first, the smallest 
last, and the right angle is to the left above. 
Figs. 12 and 13 are forms of mediation of 10 
and II. 

The child should be induced to find Figs. 
IT to 13 himself Leading him to understand 
the points of Fig. 10 exactly, he will have no 
difficulty in representing the opposite. Instead 
of drawing the smallest line first, he will draw 
the longest ; instead of drawing it downward, 
he will move his pencil upward, or at least 
begin to draw on the line which is bounded 
above, and thus reach 11. By continued re- 
flection, entirely within the limits of his capa- 
bilities, he will succeed in producing 12 and 13. 



GUIDE TO KINDER-GARTNERS. 



49 



Thus, by a different way of combination of 
five perpendicular lines, four forms have been 
produced, consisting of equal parts, being, 
however, unlike, and therefore oppositionally 
alike. 

Each of these figures is a whole in itself. 
But as every thing is always part of a larger 
whole, so also these figures serve as elements 
for more extensive formations. 

In this feature of Froebel's drawing method, 
in which we progress from the simple to the 
more complicated in the most natural and 
logical manner, unite parts to a whole and 
recognize the former as members of the latter, 
discover the like in opposites, and the media- 
tion of the latter, unquestionable guarantee 
is given that the delight of the child will be 
renewed and increased, throughout the whole 
course of instruction. Let Figs. lo — 13 be 
so united that the right angles connect in 
the center (Fig. 14), and again unite them so 
that all right angles are on the outside (Fig. 
15.) Figs. 14 and 15 are opposites. No. 14 
is a square with filled inside and standing on 
one corner; No. 15 one resting on its base, 
with hollow middle. In 14 the right angles 
are just in the middle; in 15 they are the 
most outward corners. In the forms of medi- 
ation (16 and 17), they are, it is true, on the 
middle line, but in the meantime on the out- 
lines of the figures formed. In the other 
forms of mediation, (Figs. 18, 19, etc) they 
lie altogether on the middle line ; but two in 
the middle, and two in the limits of the 
figure. 

Thus we have again, in Figs. 18 — 22, four 
forms consisting of exactly the same parts, 
which therefore are equal and still have qual- 
ities of opposites. In the meantime, they 
are fit to be used as simple elements of fol- 
lowing formations. In Fig. 22, they are com- 
bined into a star with filled middle ; in Fig. 
23, it is shown how a star with hollow middle 
may be formed of them. (The Fig. 23, on 
Plate XXXVI., does not show the lower part; 
on Plate XXII., Fig. 97, Gift Seventh, the 
whole star is shown.) Here, too, numerous 



forms of mediation may be produced, but we 
will work at present with our simple elements. 

Owing to the similarity in the method of 
drawing to that employed in the laying of the 
right angled, isosceles triangle, it is natural 
that we should here also arrive at the so-called 
rotation figures, by grouping our triangles with 
their acute angles toward the middle (Figs. 
24 and 25), or arrange them around a hollow 
square (Figs. 26 and 27.) 

Figs. 28 and 29 are forms of mediation 
between 24 and 25, and at the same time 
between 14 and 15. 

All these forms again serve as material for 
new inventions. As an example, we produce 
Fig. 30, composed of Figs. 28 and 29. 

The number of positions in which our orig- 
inal elements (Figs. 10 — 13) can be placed 
by one another, is herewith not exhausted by 
far, as the initiated will observ^e. Simple and 
easy as this method is rendered by natural 
law^s, it is hardly necessary to refer to the tab- 
lets (Plates XXI. to XXIX..) which will sug- 
gest a sufficient number of new motives for 
further combinations. 

As previously remarked, the slate is ex- 
changed for a drawing-book as soon as the pro- 
gress of the child warrants this change. It 
aflfords a peculiar charm to the pupil to see his 
productions assume a certain durability and 
permanency enabling him to measure, by thera, 
the progress of growing strength and ability. 

So far the triangles produced by co arrange- 
ment of our five lines, were right-angled. 
Other triangles, however, can be produced 
also. This, however, requires more practice 
and security in handling the pencil. 

Figs. 31 and 32 show an arrangement of 
the 5 lines, of acute angled (equilateral) tri- 
angles ; Figs. 31 and 32 being opposites. 
Their union gives the opposites 33 and 34 ; 
finally, the combination of these two. Fig. 35. 

In the last three figures we also meet now 
the obtuse angle. This finds its separate 
representation in the manner introduced in 
Fig. 36 ; opposition according to position is 
given in Fig. 37 ; mediation in Figs. 38 and 



50 



GUIDE TO KINDER-GARTNERS. 



39, and the combination of these four ele- 
ments in one rhomboid in Fig. 40. The four 
obtuse angles are turned inwardly. Fig. 42, 
the opposite of 40, is produced by arranging 
the triangles in such a manner that the obtuse 
angles are turned outwardly. Fig. 41 pre- 
sents the form of mediation. Another one 
might be produced by arranging the 4 obtuse 
angled triangles represented in Nos. 36, 37, 
38, and 39 in such a manner as to have 39 
left above, 37 right above, 36 left below, and 

39 I 37 

38 right below. Thus : ~r\—^ 

36 I 38 

It is evident that with obtuse angled trian- 
gles, as with right angled triangles, combina- 
tions can be produced. Indeed, the pupil 
who has grown into the systematic plan of 
development and combination will soon be 
enabled to unite given elements in manifold 
ways ; he will produce stars with filled and 
hollow middle, rotation forms, etc., and his 
mental and physical power and capacity will 
be developed and strengthened greatly by 
such inventive exercise. 

Side by side with invention of forms of 
beauty and knowledge, the representation of 
forms of life, take place, in free individual ac- 
tivity. The child forms, of lines of one length, 
a plate, (Fig. 43,) or a star, (Fig. 44,) of lines 
of one and two lengths a cross, (Fig. 45,) of 
lines up to 4 lengths, it represents a coffee- 
mill, (Fig. 46,) and employs the whole material 
of perpendicular lines at his command, in the 
construction of a large building with part of a 
wall connected with it. (Fig. 47.) Equal 
consideration, however, is to be bestowed 
upon the opposite of the perpendicular, 

THE HORIZONTAL LINE. 

(PLATE XXXIX.) 

The child learns to draw lines of a single 
length below each other, then lines of 2, 3, 4, 
and 5 lengths, (Figs, i — 5.) It arranges them 
also beside each other, (Figs. 6 — 8) unites 
lines of i and 2 lengths, (Fig. 9,) of i, 2, and 
3 lengths, (Fig. 10,) of i to 4 lengths, (Fig. 1 1,) 
finally of i to 5 lengths, thereby producing 



the right angled triangle 12, its opposite 13, 
and forms of mediation 14 and 15. The 
pupil arranges the elements into a square 
with filled middle, (Fig. 16) with hollow mid- 
dle, (Fig. 17) produces the forms of mediation, 

cl a dib 

(Fig. 18, — — and — — ) and continues to 

b I d a j c 

treat the horizontal line just as it has been 
taught to do with the perpendicular. ( By turn- 
ing the Plates XXXV. to XXXVIII., the 
figures on them will serve as figures with hori- 
zontal lines.) Rotation forms, larger figures, 
acute and obtuse angled triangles can be 
formed ; forms of beauty, knowledge and life 
are also invented here, (Fig. 19, adjustable 
lamp J Fig. 20, key; Fig. 21, pigeon-house;) 
and after the child has accomplished all this, it 
arrives finally, in a most natural way, at the 

COMBINATION OF PERPENDICULAR AND 
HORIZONTAL LINES. 

(plates XL. TO XLIL) 

First, lines of one single length are com- 
bined ; we already have four forms different 
as to position, (Fig. i.) Then follow the 
combination of 2, 3, 4, 5 — fold lengths, (Figs. 
2 — 5) with each of which 4 opposites as to 
position are possible. As previously, lines of i 
to 5 — fold lengths are united to triangles, so 
now the angles are united and Fig. 6 is pro- 
duced. Its opposite, 7 and the forms of medi- 
ation, can be easily found. A union of "these 
four elements appears in the square, Fig. 8; 
opposite Fig. 9. In Fig. 8, the right angles are 
turned toward the middle, and the middle is 
full. In Fig. 9, the reverse is the case. Forms 
of mediation easily found. We have in Figs. 

a i c bid 

8 and 9 the combinations — 1 — and — |---- 



Let the following 



dib 
be constructed : 
alb die dl 



dib 



b|d d|b b |d d 
b I c aid 



b ' b c ' a I d ' 



GUIDE TO KINDER-GARTNERS. 



If perpendicular and horizontal lines can 
be united only to form right angles, we have 
previously seen that perpendicular as well as 
horizontal lines may be combined to obtuse 
and acute angled triangles. The same is pos- 
sible, if they are united. Fig. lo gives us an 
e-xample. All perpendicular lines are so ar- 
ranged as to form obtuse angled triangles. By 
their combination with the horizontal lines, 
the element lo" is produced, its opposite lo'', 
and the forms of mediation io'= and lo'' whose 
combination forms Fig. lo. 

As in Fig. lo, the perpendicular lines form 
an obtuse angled triangle, so the horizontal 
lines, and finally both kinds of lines can at 
the same time be arranged into obtuse angled 
triangles. 

Thus a series of new elements is produced, 
whose systematic employment the teacher 
should take care to facilitate. (The scheme 
given in the above may be used for this 
purpose.) 

So far we have only formed angles of lines 
equal in length ; but lines of unequal lengths 
may be combined for this purpose. Exactly 
in the same manner as lines of a single length 
were treated, the child now combines the line 
of a single length with that of two lengths, 
then, in the same way, the line of two lengths 
with that of four lengths, that of three with 
that of six, that of four with that of eight, and 
finally, the line of five lengths with that of ten. 
■ The combination of these angles affords new 
elements with which the pupil can continue 
to form interesting figures in the already well- 
known manner. Figs, ii and 12, on Plate 
XL., are such fundamental forms ; the de 
velopment of which to other figures will give 
rise to many instructive remarks. These fig- 
ures show us that for such formations the 
horizontal as well as the perpendicular line 
may have the double length. Fig. 11 shows 
the horizontal lines combined in such a way 
as if to form an acute-angled triangle. They, 
however, form a right-angled triangle, only the 
right angle is not, as heretofore, at the end 
of the longest line, but where? An acute- 



angled triangle would result, if the horizontal 
lines were all two net-squares distant from 
each other. Then, however, the perpendicular 
lines viould form an obtuse-angled triangle. 

Important progress is made, when we com- 
bine horizontal and perpendicular lines in 
such a way that by touching in two points 
they form closed figures, squares and oblongs. 

First, the child draws squares of one- 
length's dimension, then of two-lengths, of 
three, four and five lines. These are combined 
then as perpendicular lines were combined 
also I- with 2-, the i^, 2^ and 3^ etc. These 
combinations can be carried out in a perpen- 
dicular direction, when the squares will stand 
over or under each other; or in horizontal, 
when the squares will stand side by side ; or, 
finally, these two opposites may be combined 
with one another. 

Fig. 13° shows as an example a combina- 
tion of four squares in a horizontal direction ; 
13'' is the opposite ; c and d are forms of me- 
diation. 

In Fig. 14*, squares of the first, second and 
third sizes are combined, perpendicularly and 
horizontally, forming a right angle to the 
right below ; b is the opposite, (angle left 
above ;) c and d are forms of mediation. The 
same rule is followed here as with the right 
angle formed by single lines. The simple 
elements are combined with each other into a 
square with full or hollow middle, etc. ; and 
from the new elements thus produced larger 
figures are again created, as the example Fig. 
15, Plate XLL, illustrates. From the four 
elements 14"''"', the figure 15* and its opposite 
B are constructed, (analogous to the manner 
employed with Fig. 28, Plate XXXVII.,) a two- 
fold combination of which resulted in Fig. 15. 
Squares of from one to five length lines of 
course admit of being combined in similar 
manner. Each essentially new element should 
give rise to a number of exercises, conditioned 
only by the individual ability of the child. It 
must be left to the faithful teacher, by an 
earnest observation and study of her pupils, 
to find the right extent, here as everywhere in 



52 



GUIDE TO KINDER- GARTNERS. 



their occupations. Indiscriminate skipping 
is not allowed, neither to pupil nor teacher ; 
each following production must, under all cir- 
cumstances be derived from the preceding one. 

As the square was the result of angles 
formed of lines of equal length, so also with 
the oblong. Here too the child begins with 
the simplest. It forms oblongs, the base of 
which is a single line, the height of which is a 
line of double length. It reverses the case 
then. Base line 2, height single length. Re- 
taining the same proportions, it progresses to 
larger oblongs, the height of which is double 
the size of its base, and vice versa, until it 
has reached the numbers 5 and 10. 

It is but natural that these oblongs, stand- 
ing or lying, should also be united in perpen- 
dicular, and horizontal directions. Each form 
thus produced again assumes four different 
positions, and the four elements are again 
united to new formations, according to the 
rules previously explained. Fig. 16" shows an 
arrangement of standing oblongs, in horizontal 
directions. The opposite would contain the 
right angle, at a to the right below — to the 
left above ; 16° would be one form of media- 
tion, a second one, (opposite of 16^) would 
have its right angle to the right above. 

Fig. 17 shows a combination of lying ob- 
longs, in a perpendicular direction. Fig. iS, 
shows oblongs in perpendicular and horizon- 
tal directions. Fig. 19, a combination of stand- 
ing and lying oblongs, the former being ar- 
ranged perpendicularly, the latter, horizon- 
tally. 

In Fig. 20, we find standing oblongs so 
combined that the form represents an acute 
angled triangle ; a and b are the only possible 
opposites in the same. 

These few examples may suffice to indicate 
the abundance of forms which may be con- 
structed with such simple material as the 
horizontal and perpendicular lines, from i to 
5 lengths, (and double.) 

It is the task of the educator to lead the 
learner to detect the elements, logically, in 
order to produce with them, new forms in 



unlimited numbers, within the boundaries of 
the laws laid down for this purpose. 

But even without using these elements, the 
child will be able, owing to continued practice, 
to represent manifold forms of life and beauty, 
partly by its own free invention, partly by 
imitating the objects it has seen before. As 
samples of the former, Plate XLIL, Fig. 27, 
shows a cross. Fig. 29, a triumphal gate. Fig. 
30, a wind-mill, of the latter, Fig. 21 — 24, and 
28, show samples of borders ; Fig. 25 and 26, 
show other simple embellishments. As the 
perpendicular line conditioned its opposite, 
the horizontal line, both again condition their 
mediation. 

THE OBLIQUE LINE. 
(plates xliii. to xlv.) 

Our remarks here can be brief as the ope- 
rations are nothing but a repetition of those 
in connection with the perpendicular line. 

The child practices the drawing of lines 
from I to 5 lengths, (Plate XLIII., i to 5,) 
and combines these, receiving thereby 4 op- 
positionally equal right angled triangles, (Fig. 
6 — 9,) of which it produces a square, (Fig. 10,) 
its opposite, (Fig. 11,) forms of mediation, and 
finally large figures. 

Then the lines are arranged into obtuse 
angles, and the same process gone through 
with them. 

With these, as in Fig. 13, its opposite 16, 
and its forms of mediation, 14 and 15, the 
obtuse angles will be found at the perpendic- 
ular middle line, or as in 17, at the horizontal 
middle line. By a combination of 15 and 17, 
we produce a star, 19. Finally we have also, 
reached here the formation of the acute 
angled triangle, (Fig. 18.) The oblique line 
presents particular richness in forms, as it 
may be a line of various degrees of inclina- 
tion. It is an oblique of the first degree 
whenever it appears as the diagonal of a 
square, as in Figs, i — 19. When it appears 
as the diagonal of an oblong, it is either an 
oblique of the 2d, 3d, 4th, or 5lh degree, ac- 
cording to the proportions of the base line. 



GUIDE TO KINDER-GARTNERS. 



53 



and height of tlie oblong, i to 2, i to 3, i to 
4, I to 5. 

In Fig. 20°, obliques of the second degree 
are united to a right-angled triangle. 20" is 
the opposite, 20° and d form mediations. 

In Fig. 21, the same lines are united in an 
obtuse angled triangle. In Fig. 22, they finally 
form an acute angle. 

In all these cases, the obliques were diag- 
onals of standing oblongs. They may just as 
well be diagonals of lying oblongs. Fig. 23, 
in which obliques from the first to the fifth 
degree are united, will illustrate this. The 
obliques are here arranged one above the 
other. In Fig. 24, the members a and b show 
a similar combination ; the obliques, however, 
are arranged beside one another ; the mem- 
bers, c and d, are formed of diagonals of stand- 
ing oblongs. 

Obliques of various grades can be united 
with one point, when the elements in Fig. 25, 
will be produced, which requires the other 
elements, b, c, and d, to form this figure, the 
opposite of which would have to be formed 

bid 
according to the formula, — — , beside which 
c I a 

c I a 
the forms of mediation would appear as — — 
b 1 d 
dlb 
(Fig. 26) and — — . 
a 1 c 

As in this case, lying figures are produced, 
standing ones can be produced likewise. 
Each two of the elements thus received may 
be united, so that all obliques issue from one 
point, as in Fig. 27, and in its opposite. Fig. 28. 

An oppositional combination can also take 
place, so that each two lines of the same 
grade meet, (Fig. 29.) The combination of 
obliques with obliques to angles, to squares 
and oblongs now follow, analogous to the 
method of combining oblongs, perpendicular 
and horizontal lines. Finally the combination 
of perpendicular and oblique, horizontal and 
oblique lines to angles, rhombus and rhomboid 
■is introduced. 

With these, the child tries his skill in pro- 



ducing forms of life : Fig. 40, gate of a for- 
tress; 41, church with school-house and cem- 
etery wall, and forms of beauty: Figs. 30 — 39. 
The task of the Kinder -Garten and the 
teacher has been accomplished, if the child 
has learned to manage oblique lines of the 
first and second degree skillfully. All given 
instaiction which aimed at something beyond 
this, was intended for the study of the teacher 
and the Primary Department, which is still 
more the case in regard to — 

THE CURVED LINE. 
(plate -\LVI.) 

Simply to indicate the progress, and to give 
Froebel's system of instruction in drawing 
complete, we add the following, and Plate 
XLVI. in illustration of it. 

First, the child has to acquire the ability to 
draw a curved line. The simplest curved line 
is the circle, from which all others may be 
derived. 

However, it is difficult to draw a circle, and 
the net on slate and paper do not afford suffi- 
cient help and guide for so doing. But on 
the other hand, the child has been enabled to 
draw squares, straight and oblique lines, and 
with the assistance of these it is not difficult 
to find a number of points which lie on the 
periphery of a circle of given size. 

It is known that all corners of a quadrangle 
(square or oblong) lie in the periphery of a 
circle whose diameter is the diagonal of the 
quadrangle. In the same manner all other 
right angles constructed over the diameter, 
are periphery angles, affording a point of the 
desired circular line. It is therefore nec- 
essary to construct such right angles, and this 
can be done very readily with the assistance 
of obliques of various grades. 

Suppose we draw from point a (Fig. i) an 
oblique of the third degree, as the diagonal 
of a standing oblong ; draw then, starting 
from point c, an oblique of the third degree, as 
diagonal of a lying oblong, and continue both 
these lines. They will meet in point a, and 
there form a right angle. 



54 



GUIDE TO KINDER-GARTNERS. 



All obliques of the same degree, drawn 
from opposite points, will do the same as 
soon as the one approaches the perpendicular 
in the same proportion in which the other 
comes near the horizontal, or as soon as the 
one is the diagonal of a standing, the other 
of a lying oblong. 

The lines Aa and Cc are obliques of the 
third, Ab and Cb of the second, Af and C/ 
of the third degree, etc., etc. In this manner 
it is easy to find a number of points, all of 
which are points in the circular line, intended 
to be drawn. Two or three of them over 
each side, will suffice to facilitate the drawing 
of the ciRCUMscribing circle, (Fig. 2.) In like 
manner, the iNXERscribing circle will be ob- 
tained by drawing the middle transversals of 
the square, (Fig. 3,) and constructing from 
their end-points angles in the previously de- 
scribed manner. 

After the pupil has obtained a correct idea 
of the size and form of the circle, whose ra- 
dius may be of from one to five lengths, it 
will divide the same in half and quarter cir- 
cles, producing thereby the elements for its 
farther activity. 

The course of instruction is here again the 
same as that in connection with the perpen- 
dicular line. The pupil begins with quarter 
circles, radius of which is of a single length. 
Then follow quarter circles with a radius of 
from two to five lengths. By arrangement of 
these five quarter circles, four elements are 
produced, which are treated in the same man- 
ner as the triangles produced by arrangement 
of five straight lines. The segments may be 
parallel, and the arrangement may take place 
in perpendicular and horizontal direction, (Fig. 
4 and 5,) or they may, like the obliques of va- 
rious degrees, meet in one point, as in Fig. 8, 
of which Figs. 4 and 5 are examples. 



Fig. 6 represents the combination of the 
elements a and (/ as a new element ; Fig. 7, 
the combination of d and c. In Fig. 8 the 
arrangement finally takes place in oblique 
direction, and all lines meet in one point. 

The quarter circle is followed by the half 
circle 9, 10, 11 ; then the three-fourths circle 
(Fig. 12), and the whole circle, as shown in 
Fig. 13- 

With the introduction of each new line, the 
same manner of proceeding is observed. 

Notwithstanding the brevity with which we 
have treated the subject, we nevertheless 
believe we have presented the course of in- 
struction in drawing sufficiently clearly and 
forcibly, and hope that by it we have made 
evident : 

1. That the method described here is per- 
fectly adapted to the child's abilities, and fit 
to develop them in the most logical manner ; 

2. That the abundance of mathematical 
perceptions offered with it, and the constant 
necessity for combining according to certain 
laws, can not fail to surely exert a wholesome 
influence in the mental development of the 
pupil ; 

3. That the child thus prepared for future 
instruction in drawing, will derive from such 
instruction more benefit than a child prepared 
by any other method. 

Whosoever acknowledges the importance 
of drawing for the future life of the pupil — 
may he be led therein by its significance for 
industrial purposes, or resthetic enjoyment, 
which latter it may afford even the poorest ! — 
will be unanimous with us in advocating an 
early commencement of this branch of in- 
struction with the child. 

If there be any skeptics on this point, let 
them try the experiment, and we are sure they 
will be won over to our side of the question. 



THE ELEVENTH AND TWELFTH GIFTS. 



MATERIAL FOR PERFORATING AND EMBROIDERING. 

(PLATES .\LVII. TO L.) 



It is claimed by us that all occupation ma- 
terial presented by Froebel, in the Gifts of the 
Kinder-Garten, are, in some respects, related 
to each other, complementing one another. 
What logical connection is there between the 
occupation of perforating and embroidering, 
introduced with the present and the use of 
the previously introduced Gifts of the Kinder- 
Garten ? This question may be asked by 
some superficial enquirer. Him we answer 
thus : In the first Gifts of the Kinder-Garten, 
the solid mass of bodies prevailed ; in the fol- 
lowing ones the plane ; then the embodied line 
was followed by the drawn line, and the occu- 
pation here introduced brings us down to the 
point. With the introduction of the per- 
forating paper and pricking needle, we have 
descended to the smallest part of the whole — 
the extreme limit of mathc?natical divisibility ; 
and in a playing manner, the child followed 
us unwittingly, on this, in an abstract sense, 
difficult journey. 

The material for these occupations is a 
piece of net paper, which is placed upon 
some layers of soft blotting paper. The 
pricking or perforating tool is a rather strong 
sewing needle, fastened in a holder so as to 
project about one-fourth of an inch. Aim of 
the occupation is the production of the beau- 
tiful, not only by the child's own activity, but 
by its own invention. Steadiness of the eye 
and hand are the visible results of the occu- 
pation which directly prepares the pupil for 
various kinds of manual labor. The per- 
forating, accompanied by the use of the 



needle and silk, or worsted, in the way em- 
broidery is done, it is evident in vi'hat direc- 
tion the faculty of the pupil may be developed. 

The method pursued with this occupation 
is analogous to that employed in the drawing 
department. Starting from the single point, 
the child is gradually led through all the 
various grades of difficulty ; and from step to 
step its interest in the work will increase, 
especially as the various colors of the em- 
broidered figures add much to their liveliness, 
as do the colored pencils in the drawing 
department. 

The child first pricks perpendicular lines 
of two and three lengths, then of four and five 
lengths, (Figs. 2 and 3.) They are united to 
a triangle, opposites and forms of mediation 
are found, and these again are united into 
squares with hollow and filled middle, (Figs. 
4 and 5.) The horizontal line follows, (Figs. 
6 — 8,) then the combination of perpendicu- 
lar and horizontal to a right angle in its four 
oppositionally equal positions, (Figs. 9 — 12.) 
The combination of the four elements present 
a vast number of small figures. If the exter- 
nal point of the angle of 9 and 10 touch one 
another, the cross (Fig. 13) is produced; if 
the end points of the legs of these figures 
touch, the square is made, (Fig. 14.) By 
repeatedly uniting 9 and 12 Fig. 15 is pro- 
duced, and by the combination of all four 
angles Figs. 16 and 17. According to the 
rules followed in laying figures with tab- 
lets of Gift Seven, and in drawing, or by a 
simple application of the law of opposites, the 



56 



GUIDE TO KINDER-GARTNERS. 



child will produce a large number of other 
figures. 

The combination of lines of i and 2 lengths 
is then introduced, and standing and lying 
oblongs are formed, (Figs. 18 and ig,) etc. 
The school of perforating, per se, has to con- 
sider still simple squares and lying and 
standing oblongs, consisting of lines of from 
2 to 5 lengths.- In order not to repeat the 
same form too often, we introduce in Pigs. 
2 1 — 3 1 a series of less simple ; containing, 
however, the fundamental forms, showing in 
the meantime the combination of lines of 
various dimensions. 

In a similar way, the oblique line is now 
introduced and employed. The child pricks 
it in various directions, commencing with a 
one length line, (Figs. 32 — 35,) combines it to 
angles, (Figs. 36 — 39,) the combination of 
which will again result in many beautiful 
forms. Then follows the perforating of ob- 
lique lines of from 2 to 5 lengths, (a single 
length containing up to seven points,) which 
are employed for the representation of bor- 
ders, corner ornaments, etc., (Figs. 42 — 45, 
61.) The oblique of the second degree is 
also introduced, as shown in Figs. 46 and 47, 
and the peculiar formations in Figs. 48 — 51. 

Finally, the combination of the oblique 
with the perpendicular line, (Figs. 52 and 54,) 
and with the horizontal, (Figs. 53 and 55,) or 
with both at the same time, (Figs. 56 — 60,) 
takes place. The conclusion is arrived at in 
the circle (Fig. 62) and the half circle (Figs. 
63-69.) 

All these elements may be combined in 
the most manifold manner, and the inventive 
activity of the pupil will find a large field in 
producing samples of borders, corner-pieces, 
frames, reading marks, etc., etc. 

When it is intended to produce amything of 
a more complicated nature, the pattern should 
be drafted by pupil or teacher upon the net 
paper previous to pricking. In such cases, 
it is advisable and productive of pleasure to 
the pupils, if beneath the perforating paper 
another one doubly folded is laid, to have the 



pattern transferred by perforation upon this 
paper in various copies. Such little produc- 
tions may be used for various purposes, and 
be presented by the children to their friends 
on many occasions. To assist the pupils in 
this respect, it is recommended that simple 
drawings be placed in the hands of the pupils, 
which, owing to their little ability, they cer- 
tainly could not yet produce by drawing, but 
which they can well trace with their per- 
forating tool. These drawings should repre- 
sent objects from the animal and vegetable 
kingdoms, and may thus be. of great service 
for the mental development of the children. 
The slowly and carefully perforated forms 
and figures will undoubtedly be more last- 
ingly impressed upon the mind and longer 
retained by the memory, than if they were 
only described or hurriedly looked at. Plate 
XLIX. presents a few of such pictures, which 
can easily be multiplied. 

A particular explanation is required for 
Fig. 84, on Plate L. In this figure are con- 
tained shaded parts, indicating plastic forms, 
which so far have not been introduced, all 
previous figures presenting mere outlines to 
be perforated. It is supposed to be known 
that each prick of the needle causes some- 
what of an elevation on the reverse (wrong 
side) of the paper. If a number of very fine, 
scarcely visible pricks are made around a 
certain point, an elevated place will be the 
result, so much more observable, the larger 
the number of pricks concentrated on the 
spot. In this wise it is possible to represent 
certain parts of a design as standing out in 
relief It is understood that very young chil- 
dren could not well succeed in such kind of 
work. The older ones find material in Figs. 
72, 74 and 76 to try their skill in this direc- 
tion, and thereby prepare themselves for fig- 
ures like 84. 

All figures of Plates XXXIX., XLIL, and 
XLIX. may well be used for samples of per- 
forating and embroidering. 

It should be mentioned that the embroider- 
ing does not begin simultaneously with the 



GUIDE TO KINDER-GARTNERS. 



57 



perforating, but only after the children have 
acquired considerable skill in the last named 
occupation. For purposes of 

EMBROIDERING, 
The same net paper which was used for e.xer- 
cises in perforating may be employed, by fill- 
ing out the intervals between the holes with 
threads of colored silk or worsted. It will be 
sufficient for this purpose to combine the 
points of one net square only, because other- 
wise the stitches would become too short to 
be made wilh the embroideiy needle in the 
hands of children yet unskilled. For work, to 
be prepared for a special purpose, the perfor- 
ated pattern should be transferred upon stiff 
paper or bristol-board. 

Course of instruction just the same as with 
perforating. 

Experience will show that of the figures 
contained on our plates, some are more fit for 
perforating, others better adapted for embroid- 
ering. Either occupation leads to peculiar 
results. Figures in which strongly rounded 
lines predominate may be easily perforated, 
but with difficulty, or not at all be embroid- 
ered, as Figs. 75 and 77. By the process of 
embroidering, however, plain forms, as stars, 
and rosettes, are easily produced, which could 
hardly be represented, or, at best, very imper- 
fectly only, by the perforating needle. Figs. 
87 — 92, and Fig. 39 on Plate XLII. are ex- 
amples of this kind. 

To develop the sense of color in the chil- 
dren, the paper on which they embroider, 
should be of all the various shades and hues, 
through the whole scale of colors. If the 
paper is gray, blue, black, or green, let the 
worsted or silk be of a rose color, white, or- 
ange or red, and if the pupil is far enough 
advanced to represent objects of nature, as 
fruit, leaves, plants, or animals, it will be very 
proper to use in embroidering, the colors 



shown by these natural objects. Much can 
be thereby accomplished toward an early de- 
velopment of appreciation and knowledge of 
color, in which grown people, in all countries 
are often sadly deficient. It has appeared to 
some, as if this occupation is less useful than 
pleasurable. Let them consider that the ordi- 
nary seeing of objects already is a difficult 
matter, nay, really an art, needing long prac- 
tice. Much more difficult and requiring much 
more careful exercise, is a true and correct 
perception of color. 

If the bcatttifid is introduced at all as a 
means of education — and in Froebel's institu- 
tions it occupies a prominent place — it should 
approach the child in various ways ; not only 
mform, but in color, and tone also. To insure 
the desired result in this direction, we begin 
in the Kinder-Garten, where we can much 
more readily make impressions upon the 
blank minds of children, than at a later pe- 
riod when other influences have polluted their 
tastes. 

For this reason, we go still another step 
farther, and give the more developed pupil a 
box with the three fundamental colors, show- 
ing him their use, in covering the perforated 
outlines of objects with the paint. Children 
like to occupy themselves in this manner, and 
show an increased interest, if they first pro- 
duce the drawing and are subsequently al- 
lowed to use the brush for further beautifying 
their work. 

We only give three fundamental colors, in 
order not to confound the beginner by need- 
less multiplicity, as also to teach how the sec- 
ondary colors,may be produced by mixing the 
primarj'. 

The perforating and embroidering are be- 
gun with the children in the Kinder-Garten, 
when they have become sufficiently prepared 
for the perception of forms by the use of their 
building-blocks and staffs. 



THE THIRTEENTH GIFT. 



MATERIAL FOR CUTTING PAPER AND MOUNTING PIECES TO PRODUCE 
FIGURES AND FORMS. 



(PLATES 

The labor, or occupation alphabet, pre- 
sented by Froebel in his system of education, 
cannot spare the occupation, now introduced 
— the cutting of paper — the transmutation of 
the material by division of its parts, notwith- 
standing the many apparently well-founded 
doubts, whether scissors should be placed into 
the hands of the child at such an early age. 
It will be well for such doubters to consider : 
Firstly, that the scissors which the children 
use, have no sharp points, but are rounded at 
their ends, by which the possibilities of doing 
harm with them are greatly reduced. Sec- 
ondly, it is expected that the teacher employs 
all possible means to watch and superintend 
the children with the utmost care during their 
occupation with the scissors. Thirdly, as it 
can never be prevented, that, at least, at times 
scissors, knives and similar dangerous objects 
may fall into the hands of children, it is of 
great importance to accustom them to such, 
by a regular course of instruction in their use, 
which, it may be expected, will certainly do 
something to prevent them from illegitimately 
applying them for mischievous purposes. 

By placing material before them from which 
the child produces, by cutting according to 
certain laws, highly interesting and beautiful 
forms, their desire of destroying with the scis- 
sors will soon die out, and they, as well as 
their parents, will be spared many an unpleas- 
ant experience, incident upon this childish in- 
stinct, if it were left entirely unguided. 

As material for the cutting, we employ a 
square piece of paper of the size of one-six- 



teenth sheet, similar to the folding sheet. 
Such a sheet is broRen diagonally, (Plate 
LXIX., Fig. 5,) the right acute angle placed 
upon the left, so as to produce four triangles 
resting one upon another. Repeating the same 
proceeding, so that by so doing the two upper 
triangles will be folded upwards, the lower 
ones downwards in the halving line, eight 
triangles resting one upon another, will be 
produced, which we use as our first funda- 
mental form. This fu7ida7nental form is held, 
i?i all exercises, so that the open side, where no 
plane connects with another is always turned 
toivard the left. 

In order to accomplish a sufficient exact- 
ness in cutting, the uppermost triangle con-. 
tains, (or if it does not, is to be provided with) 
a kind of net as a guide in cutting. Dotted 
lines indicate on our plates this net-work. 

The activity itself is regulated according 
to the law of opposites. We commence with 
the perpendicular cut, come to its opposite, 
the horizontal and finally to the mediation of 
both, the oblique. 

Plates 51 — 53 indicate the abundance of 
cuts which may be developed according to 
this method, and it is advisable to arrange for 
the child a selection of the simpler elements 
into a school of cutting. 

The following selection presents, almost 
always, two opposites and their combination, 
or leaves out one of the former, as is the case 
with the horizontal cut, wherever it does not 
produce anything essentially new. 

a. Perpendicular cuts, 2, 3, 4 — 5, 6, 7. 



GUIDE TO KINDER- GARTNERS. 



59 



b. Horizontal cuts, 8, 9— (above ; above 
and below). 

c. Perpendicular and horizontal, 18, 19, 
20 — 21, 22, 23. 

d. Oblique cuts, 34, 35—36, 37, 38. 

e. Oblique and perpendicular, 51, 52, 53, 
—54, 55- 56—58- 59. 60. 

/ Oblique and horizontal, 65, 66, 67. 

g. Half oblique cuts, where the diagonals 
of standing and lying oblongs, formed of two 
net squares, serve as guides — 117, 118, 119 — 
121, 122, 123 — 125, 126, 127. 

Here ends the school of cutting, perse, for 
the first fundamental form, the right angled 
triangle. The given elements may be com- 
bined in the most manifold manner, as this 
has been sufficiently carried out in the forms 
on our plates. 

The fundamental form used for Plates LIV. 
and LV. is a six fold equilateml triangle. It 
also is produced from the folding sheet, by 
breaking it diagonally, halving the middle of 
the diagonal, dividing again in three equal 
parts the angle situated on this point of halv- 
ing. The angles thus produced will be an- 
gles of 60 degrees. The leaf is folded in the 
legs of these angles by bending the one acute 
angle of the original triangle, upwards, the 
other downwards. By cutting the protruding 
corners, we shall have the desired form of the 
si.x fold equilateral triangle, in which the en- 
tirely open side serves as basis of the triangle. 
The net for guidance is formed by division of 
each side in four equal parts, uniting the points 
of division of the base, by parallel lines with 
the sides, and drawing of a perpendicular 
from the upper point of the triangle upon its 
base. It is the oblique line, particularly which 
is introduced here. The designs and patterns 
from 133 — 145, will suffice for this purpose. 
The same fundamental form is used for prac- 
tising and performing the circular cuts, al- 
though the right angular fundamental form 
may be used for the same purpose. Both find 
their application subsequently, in a sphere of 
development only, after the child by means 
of the use of the half and whole rines, and 



drawing, has become more familiar with the 
curved line. These exercises require great 
facility in handling the scissors, besides, and 
are, therefore, only to be introduced with 
children, who have been occupied in this de- 
partment quite a while. For such it is a cap- 
ital employment, and they will find a rich 
field for operation, and produce many an in- 
teresting and beautiful form in connection 
with it. The course of development is indi- 
cated in figures 164 — 172. 

After the child has been sufficiently intro- 
duced into the cutting school, in the manner 
indicated in the above ; after his fantasy 
has found a definite guidance in the ever-re- 
peated application of the law, which protects 
him against unbounded option and choice, it 
will be an easy task to him, and a profitable 
one, to pass over to free invention, and to 
find in it a fountain of enjoyment, ever new, 
and inexhaustibly overflowing. To let the 
child, entirely without a guide, be the master 
of his own free will, and to keep all discipline 
out of his way, is one of the most dangerous 
and most foolish principles to which a misun- 
derstood love of children, alone, could bring 
us. This absolute freedom condemns the 
children, too soon, to the most insupportable 
annoyance. All that is in the child should be 
brought out by means of external influence. 
To limit this influence as much as possible is not 
to suspend it. Froebel has limited it, in a most 
admirable way by placing this guidance into the 
child itself, as early as possible ; that from one 
single incitement issues a number of others, 
within the child, by accustoming it to a lawful 
and regulated activity from its earliest youth. 

With the first perpendicular cut, which we 
made into the sheet (Fig. i,) the whole course 
of development, as indicated in the series of 
figures up to No. 132 is given, and all subse- 
quent inventions are but simple, natural com- 
binations of the element presented in the 
'■^school." Thus a logical connection prevails 
in these formations, as among all other means 
of education, hardly any but mathematics 
may afford. 



60 



GUIDE TO KINDER- GARTNERS. 



Whereas the activity of the cutting itself, 
the logical progress in it advances a most 
beneficial influence upon the intellect of the 
pupil, the results of it will awaken his sense 
of beauty, his taste for the symmetrical, his 
appreciation of harmony in no less degree. 
The simplest cut already yields an abundance 
of various figures. If we make as in Fig. 5, Plate 
LI., two perpendicular cuts, and unfold all 
single parts, we shall have a square with 
hollow middle, a small square, and finally the 
frame of a square. If we cut according to 
Fig. 6, we produce a large octagon, four 
small triangles, four strips of paper of a trape 
zium form, nine figures altogether. 

All these parts are now symmetrically ar- 
ranged according to the law: union of op- 
posites — here effected by the position or direc- 
tion of the parts, relative to the center — 
and after they have been arranged in this 
manner, the pupils will often express the de- 
sire to preserve them in this arrangement. 
This natural desire finds its gratification by 

MOUNTING THE FIGURES. 
As separation always requires its opposite, 
uniting, so the cutting requires mounting. 
Plates LVI. to LVIII. present some examples 
from which the manner in which the results 
of the cutting may be applied, can be easily 
derived. With the simpler cuts, the clippings 
are to be employed, but if a main figure is 



complete and in accordance with the claims 
of beauty in itself, itwould be foolish to spoil 
it, by adding the same. 

This occupation, also, can be made sub- 
servient to influence the intellectual develop- 
ment of the child by requiring it to point 
out all manners in which these forms may 
be arranged and put together. (Plate LVI., 
Fig- S-) 

In order to increase the interest of the chil- 
dren, to give a larger scope to their inventive 
power, and at the same time, to satisfy their 
taste and sense of color, they may have paper 
of various colors and be allowed to e.xchange 
their productions among one another. 

Both these occupations, cutting and mount- 
ing, are for Kinder Garten as well as higher 
grades of schools. For older pupils, the cut- 
ting out of animals, plants and other forms of 
life will be of interest, and silhouettes even 
may be prepared by the most expert. 

It is evident that not only as a 'simple 
means of occupation for the children, during 
their early life, but as a preparation for many 
an occupation in real life, the cutting of paper 
and mounting the parts to figures, as intro- 
duced here, are of undeniable benefit. 

The main object, however, is here, as in all 
other occupations in the Kinder-Garten, de- 
velopment of the sense of beauty, as a prep- 
aration for subsequent performance in and 
enjoyment of art. 



THE FOURTEENTH GIFT. 



MATERIAL FOR BRAIDING OR WEAVING. 



(tlates lix. to lx>v.) 



Braiding is a favorite occupation of chil- 
dren. The child instinctively, as it were, likes 
everything contributing to its mental and 
bodily development, and few occupations may 



claim to accomplish both, better than the oc- 
cupation now introduced. It requires great 
care, but the three year old child may already 
see the result of such care, whereas even from 



GUIDE TO KINDER-GARTNERS. 



6l 



twelve to fourteen years old pupils often have 
to combine all their ingenuity and persever- 
ance to perform certain more complicated 
tasks in the braiding or weaving department. 
It does not develop the right hand alone, the 
left also finds itself busy most of the time. It 
satisfies the taste of color, because to each 
piece of braiding, strips of at least two differ- 
ent colors belong. It excites the sense of 
beauty because beautiful, /. e , symmetrical, 
forms are produced ; at least their production 
is the aim of this occupation. The sense and 
appreciation of number are constantly nour- 
ished, nay, it may be asserted, that there is 
hardly a better means of affording percep- 
tions of numerical conditions, so thorough, 
founded on individual experience and ren- 
dered more distinct by diversity in form and 
color, than '^braiding." The products of the 
child's activity, besides, are readily m.ade use- 
ful in practical life, affording thereby capital 
opportunities for expression of its love and 
gratitude, by presents prepared by its own 
hand. 

The material used for this occupation are 
sheets of paper prepared as shown on Plate 
LIX., strips of paper, and the braiding needle, 
also represented on Plate LIX. 

A braid work is produced by drawing with 
the needle a loose strip (white) through the 
strips of the braiding sheet, (green) so that a 
number of the latter will appear over, another 
under the loose strip. These numbers are 
conditioned by the form the work is to as- 
sume. As there are but two possible ways 
in which to proceed, either lifting up, or pres- 
sing down, the strips of the braiding sheet, 
the course to be taken by the loose strip is 
easily expressed in a simple formula. All 
varieties of patterns are expressible in such 
formulas, and therefore easily preserved and 
communicated. 

The simplest formula of course, is when one 
strip is raised and the next pressed down. 
We express this formula by i u (up), i d 
(down). All such formulas in which only two 
figures occur, are called simple formulas ; 



combination formulas, however, are such as 
contain a combination of two or more such 
simple formulas. 

But with a single one of such formulas, no 
braid work can yet be constructed. If we 
should, for instance, repeat with a second, 
third, and fourth strip, i u, i d, the loose 
strips would slip over one another at the 
slightest handling, and the strips of the braid- 
ing sheet and the whole work, drop to pieces 
if we should cut from it, the margin. In do- 
ing the latter, we have, even with the most 
perfect braidwork, to employ great care ; but 
it is only then a braid or weaving work exi^sts 
— when all strips are joined to the whole by 
other strips, and none remain entirely de- 
tached. 

To produce a braid work, we need at least 
two formulas, which are introduced alternately. 
Proceeding according to the same fundamen- 
tal law which has led us thus far in all our 
work, we combine first with i ;/, i d, its oppo- 
site \ d, \ u. 

Such a combination of braiding formulas 
by which not merely a single strip, but the 
whole braid work, is governed, is a braiding 
scheme. 

Braiding formulas, according to which the 
single strip moves, are easily invented. Even 
if one would limit one's self to take up or press 
down no more than five strips, (and such a 
limitation is necessary, because otherwise the 
braiding would become too loose,) the follow- 
ing thirty formulas M'ould be the result : 

1, lu id 9, 3u id 17, 4u 2d 24, 5d lu 

2, id lu 10, 3d lu 18, 4d 2u 25, 5u 2d 

3, 2u 2d n, 3u 2d 19, 4U 3d 26, 5d 2u 

4, 2d 2u 12, 3d 2u 20, 4d 3u 27, 5u 3d 

5, 2u id 13, 4u 4d 21, 5u 5d 28, 5d 3U 

6, 2d lu 14, 4d 4u 22, 5d 5u 29, 5U 4d 

7, 3u 3d 15, 4U id 23, 5u id 30, 5d 4U 

8, 3d 3u 16, 4d lu 

From these thirty formulas, among which are 
always two oppositionally alike, as for in- 
stance, I and 2, 9 and 10, 25 and 26, hun- 
dreds of combined, or combination formulas 
can be formed by simply uniting two of them. 
In the beginning it is advisable to combine 



62 



GUIDE TO KINDER-GARTNERS. 



such as contain equally named numbers either 
even or odd. The following are some ex- 
amples : 

Formulas i and 3, lu id, 2u 2d. 

" I and 5, III id, 2u id. 

" I and 7, III id, 3U 3d. 

" I and 9, lu id, 3U id. 

" I and II, lu id, 3U 2d. 

" I and 13, III id, 4U 4d. 

" I and 15, lu id, 411 id. 

" I and 17, lu id, 4U 2d. 

" I and 19, lu id, 4U 3d. 

" I and 21, lu id, 5U 5d. 

" I and 23, lu id, 5U id. 

I and 25, III Id, 511 2d. 

" I and 27, lu id, 5U 3d. 

" I and 29, lu id, 5u 4d. 

If we also add the formulas under the even 
numbers in the given thirty, we have to read 
them inversely. Thus : 

Formulas I and 6, lu id, lu 2d. 

" I and 10, lu id, lu 3d. 

" I and 12, III id, 2u 3d. 

" I and 16, lu id, lu 4d. 

" I and iS, lu id, 2u 4d. 

" I and 20, ui id, 3U 4d. 

" I and 24, III id, lu 5d. 

" I and 26, lu id, 2u 5d. 

I and 28, lu id, 3U 5d. 

" I and 30, lu id, 4U 5d. 

By a combination of one single formula 
with the twenty-four others, we receive new 
combination formulas and see that inventing 
formulas is a simple mathematical operation, 
regulated by the laws of combination. 

Much more difficult it is to invent braiding 
schemes. Not to dwell too long on this point, 
we introduce the reader to the course shown 
in pictures on our plates, which is arranged so 
systematically that either as a whole or with 
some omissions, it may be worked through 
with children from three to six years, as a 
braiding school. It begins with simple formu- 
las and by means of the law of oppbsites is 
carried out to the most beautiful figures. 

Formula i, lu id, (Fig. i,) is first intro- 
duced; opposite in regard to number is 2u 
2d, (Fig. 2). In Fig. 3 the numbers i and 2 
are combined ; Fig. 4 is a combination of 
Figs. I and 2 ; Fig. 5 a combination of Figs. 



I and 3 by combining the simple formulas. 
If we examine Fig. 5, the number 3 makes 
itself prominent in the strips running ob- 
liquely. In Fig. 6 it occurs independently as 
opposite to I and 2, and then follows in Figs. 
7-15 a series of mediative forms all uniting 
the opposites in regard to number. In all 
these patterns the squares or oblongs pro- 
duced, are arranged perpendicularly under, or 
horizontally beside, one another. Except in 
Fig. I, the oblique line appears already be- 
side the horizontal and perpendicular. Thus, 
this given opposite of form is prevailing on 
Plate LXL, and we apply here the same for- 
mulas as on Plate LX., with the difference, 
however, that we need only one formula, 
which in the second, third strip, etc], always 
begins one strip later or earlier. Thus in 
Fig. 16, the formula 2U 2d (as in Fig. 2) is 
carried out. The dark and light strips of the 
pattern run here from right above to left be- • 
low. Opposite of positioji to Fig. 16, is 
shown in Fig. 17, where both run the oppo- 
site way. Fig. 18 shows combination, and 
Fig. 19 double combination. In opposition 
to the connected oblique lines, the broken line 
appears in Fig. 20. As the formula 2U 2d 
has furnished us five patterns, so the formula 
of Fig. 3, lu 2d, furnishes the series 21 — 25. 
Nos. 21 and 22 are opposites as to direction. 
Fig. 23 shows the combination of these op- 
posites. Figs. 24 and 25, opposites to one 
another, are forms of mediation between 21 
and 22. With them for the first time a mid- 
dle presents itself. 

While in Figs. 21 — 26 the dark color is 
prevailing. Figs. 26 — 28 show us predom- 
inantly, the light strip, consequently the op- 
posite in color. In 29 — 32, formulas from Figs. 
3 — 5 are employed. Fig. 29 requires an op- 
posite of direction, a pattern in which the strips 
run from left above to right below. Fig. 30 
gives the combination of both directions and 
Figs. 31 and 32 are at the same time op- 
posites as to direction and color. 

It is obvious that each single formula can 
be used for a whole series of divers patterns, 



GUIDE TO KINDER-GARTNERS. 



63 



and the invention of these patterns is so easy 
that it will suffice if we introduce each new 
formula very briefly. • 

Fig- 33 's a form of mediation for the for- 
• mula 3U 3d ; Fig. 34 shows a different appli- 
cation of the same formula. In Fig. 35 the 
broken line appears again, but in opposition 
to 20, it changes its direction with each break. 
In Figs. 36 — 40 the formulas of Figs. 7, 8, 
10, II, and 13 are carried out. The braiding 
school, J>er se, is here concluded. Whoever 
may think it too extensive may select from it 
Nos. I, 2, 3, 6, 7, 10, 16, 17, 18, 21, 26, 24, 
25, 33, and 34. 

But if any one would like still to enlarge 
upon it, she may do so by working out, for 
each single formula the forms or patterns 
16, 17, 18, 19, 24 and 25, and continue the 
school to the number 5. The number of pat- 
terns will be made, thereby, ten times larger. 

Another change, and enlargement of the 
school may be introduced by cutting the 
braiding strips, as well as those of the braiding 
sheet, of different widths. We can, thereby, 
represent quite a number of patterns after 
the same formula, which are, however, essen- 
tially different. This is particularly to be 
recommended with very small children, who 
necessarily will have to be occupied longer 
with the simple formula lu id. But for more 
developed braiders, such change is of interest, 
because by it a great variety of forms may 
be produced which may be rendered still 
more interesting and attractive, by a variety 
of colors in the loose braiding strips. 

With patterns that have a middle, as 24 
and 28, it is advisable to let the braiding be- 
gin (especially with beginners,) with the mid- 
dle strip, and then to insert always one strip 
above, and one below it. 



It is not unavoidably necessary that the 
school should be finished from beginning to 
end, as given here. Quite the reverse. The 
pupil, after having successfully produced some 
patterns, may be afforded an opportunity for 
developing his skill by his own invention, in 
trying to form, by braiding a cross, with hol- 
low middle, (Fig. 41,) a standing oblong, (42,) 
a long cross, (43,) a small window, (45,) etc. 

Plate LXIIL, presents some patterns which 
may be used for wall-baskets, lamp tidies, 
book-marks, etc., and which may easily be 
augmented by such as have acquired more 
than ordinary skill. 

Finally, Plate LXIV. shows in figures i — 3, 
obliquely intertwined strips, representing the 
so called free-braiding, the braiding without 
braiding sheet. This is done in the following 
manner : Cut two or more long strips (Fig. 4) 
of a quarter sheet of colored paper, (green,) 
and fold to half their length, (Fig. 5,) cut 
then, of differently colored paper, (white,) 
shorter strips, afso fold these to half their 
length. Put the green strips side by side of 
one another, as shown in Fig. 7, so that the 
closed end of the one strip lies above, and 
that of the other below, (7^^.) Then take 
the white strip, bend it around strip i, and 
lead it through strip 2, (Fig. 8.) The second 
strip is applied in an opposite way, laying it 
around 2, and leading it through i. Em- 
ploying four instead of two green strips, the 
bookmark. Fig. 9, will be the result. The 
protruding ends are either cut or scolloped. 
By introducing strips of different widths, 
a variety of patterns can also here be pro- 
duced. 

Instead of paper, glazed muslin, leather, 
silk or woolen ribbon, straw and the like may 
be used as material for braiding. 



THE FIFTEENTH GIFT. 



THE INTERLACING SLATS. 



(plates lxv. and lxvi.) 



Froebel, in his Gifts of the Kinder-Garten, 
does not present anything perfectly new. All 
his means of occupation are the result of care- 
ful observation of the playing child. But he 
has united them in one corresponding whole ; 
he has invented a method, and by this method 
presented the possibility of producing an ex- 
haustless treasure of formations which, each 
influencing the mind of the pupil in its pecu- 
liar way, effect a development most harmoni- 
ous and thorough of all the mental faculties. 
The use of slats for interlacing is an occupa- 
tion already known to our ancestors, and who 
has not practiced it to some extent in the 
days of childhood ? But who has ever suc- 
ceeded in producing more than five or six 
figures with them ? Who has ever derived, 
from such occupation, the least degree of that 
manual dexterity and mental development, 
inventive power and talent of combination, 
which it affords the pupils of the Kinder-Gar- 
ten, since Froebel's method has been applied 
to the material ? 

Our slats, ten inches long, three-eighths of 
an inch broad and one-sixteenth of an inch 
thick, are made of birch or any tough wood, 
and a dozen of them are sufficient to produce 
quite a variety of figures. They form, as it 
were the transition from the plane of the tab- 
let to the line of the staffs, (Ninth Gift) differ- 
ing, however, from both, in the fact that forms 
produced by them are not bound to the plane, 
but contain in themselves a sufficient hold to 
be separated from it. 

The child first receives one single slat. Ex- 



amining it, it perceives that it is flexible, that 
its length surpasses its breadth many times, 
and again that its thickness is many times 
less than its breadth. 

Can the pupil name some objects between 
which and the slat, there is any similarity ? 

The rafters under the roof of a house, and 
in the arms of a wind-mill, and the laths of 
which fences, and certain kinds of gates, and 
lattice work are made, are similar to the slat. 

The child ascertains that the slat has two 
long plane sides and two ends. It finds its 
middle or center point, can indicate .the upper 
and lower side of the. slat, its upper and lower 
end, and its right and left side. After these 
preliminaries, a second slat is given the child. 
On comparison the child finds them perfectly 
alike, and it is then led to find the positions 
which the two slats may occupy to each other. 
They can be laid parallel with each other, so 
as to touch one another with the whole length 
of their sides, or they may not touch at all. 

They can be placed in such positions that 
their ends touch in various ways, and can be 
laid crosswise, over or under one another. 

With an additional slat, the child now con- 
tinues these experiments. It can lay various 
figures with them, but there is no binding or 
connecting hold. Therefore as soon as it at- 
tempts to lift its work from the table, it falls 
to pieces. 

By the use oifour slats, it becomes enabled 
to produce something of a connected whole, 
but this only is done, when each single slat 
coines in contact with at least three other slats. 



GUIDE TO KINDER-GARTNERS. 



65 



Two of these should be on one side, the third 
or middle one should rest on the other side 
of the connecting slat, so that here again the 
law of opposites and their mediation is fol- 
lowed and practically demonstrated in every 
figure. 

It is not easy to apply this law constantly 
in the most appropriate manner. But this 
ver}' necessity of painstaking, and the reason- 
ing, without which little success will be at- 
tained, is productive of rich fruit in the de- 
velopment of the pupil. 

The child now places the slat aa horizon- 
tally upon the table. £b is placed across it 
in a perpendicular direction ; cc in a. slanting 
direction under a and b, and eld is shoved under 
aa and over bb and under cc, as shown in Fig. i. 

This gives a connected form, which will not 
easily drop apart. The child investigates 
how each single slat is held and supported — 
it indicates the angles, which were created, 
and the figures which are bounded by the va- 
rious parts of the slats. 

To show how rich and manifold the material 
for obse'rvation and instruction given in this 
one figure is, we will mention that it contains 
twenty-four angles, of which 8 (i — 8) are 
right, 8 (9 — 16) acute, and 8 (17 — 24) obtuse 
— formed by one perpendicular slat, bb, one 
horizontal, aa, one slanting from left above 
to right below, cc, and another slanting from 
right above to left below, dd. 

Each single slat touches each other slat 
once ; two of them, aa and bb, pass over two 
and under one, and the others, cc and dd, pass 
under two and over one of the other slats, by 
which interlacing, three small figures are 
formed within the large figure, one of which 
is a figure with two right, one obtuse and one 
acute angle, (3, 6, 22, 10), and four unequal 
sides, and two others, one of which is a right 
angled triangle with two equal sides, and the 
other is a right angled triangle with no equal 
sides. 

By drawing the slats of Fig. i apart. Fig. 
2, an acute angled triangle is produced — by 
drawing them together, Fig. 3 results, from 



which the acute angled triangle, Fig. 4, can 
again be easily formed. Each of these fig- 
ures present? abundant matter for* investiga- 
tion and instructive conversation, as shown 
above in connection with Fig. i. 

The child now receives a fifth slat. Sup- 
pose we have Fig. 2, consisting of four slats 
— ready before us — we can, by adding the 
fifth slat, easily produce what appears on 
Plate LXV. as Fig. 8. 

If the five slats are disconnected, the child 
may lay two, perpendicularly at some distance 
from each other, a third in a slanting position 
over them from right above to left below, and 
a fourth in an opposite direction, v.heu the 
two latter will cross each other in their mid- 
dle. By means of the fifth slat the interlac- 
ing then is carried out, by sliding it from 
right to left under the perpendicular over the 
crossing two, and again under the other perpen- 
dicular slat, and thereby the figure 5 made firm. 

By bending the perpendicular slats together. 
Fig. 6 is produced; when the horizontal slat 
assumes a higher position, a five angled fig- 
ure appears — one of the slanting slats, how- 
ever, has to change its position also, as shown 
in Fig. 7. In Fig. 8, the horizontal slat is 
moved downward. In Fig. 9, the original 
position of the crossing slats is changed ; in 
the triangle. Fig. lo, still more, and in Figs. 
II and 12, other changes of these slats are 
introduced. 

The addition of a sixth slat enables us still 
further to form other figures from the previous 
ones — Fig. 17 can be produced from 9, 18 
from 10 or 11, 22 from 12, and then a fol- 
lowing series can be obtained by drawing 
apart and shoving together as heretofore. 

Let us begin thus : the child lays (Fig. 13) 
two slats horizontally upon the table — two 
slats perpendicularly over them ; a large 
square is produced. A fifth slat horizontally 
across the middle of the two perpendicular 
slats, gives two parallelograms, and by con- 
necting the si.xth slat from above to below with 
the three horizontal slats, so that the middle 
one is under and the two outside slats over it, 



66 



GUIDE TO KINDER-GARTNERS. 



the child will have formed four small squares, 
of equal size. 

The figures 17 and 18, (triangles,) and 19 
and 23, (hexagons,) deserve particular atten- 
tion, because they afford valuable means for 
mathematical observations. 

On Plate LXVI. we find some few ex- 
amples of seven intertwined slats, (Figs. 25 — 
28,) of eight slats, (Figs. 29 — 36,) of nine slats, 
(Figs. 37 — 40,) and often slats, (Figs. 41 — 43.) 

All we have given in the above are mere 
hints to enable the teacher and pupil to find 
more readily by individual application, the 
richness of figures to be formed with this oc- 
cupation material. 

It is particularly mathematical forms, reg- 
ular polygons, (Figs. 28, 31, 40, 42,) contem- 
plation of divisions, produced by diagonals, 
etc., planes and proportions of form, which, 
informs of knowledge, are brought before the 
eye of the pupil, with great clearness and dis- 
tinctness, by the interlacing slats. 

In the meantime, it will afford pleasure to 
behold the forms of beauty, as given in Figs. 
3°) 33; 37; nor should \\i^ forms of life be 
forgotten, as they are easily produced by a 
larger number of slats, (Fig. 39 — a fan ; 35 
and 36 — fences,) by combining the work of 
several pupils. 



The figures are not simply to be constructed 
and to be changed to others, but each of them 
is to be submitted to a careful investigation 
by the child, as to its angles, its constituent 
parts, and their qualities, and the service each 
individual slat performs in the figure as indi- 
cated with Fig. I, on page LXV. 

The occupation with this material will fre- 
quently prove perplexing and troublesome 
to the pupil ; oftentimes he will try in vain 
to represent the object in his mind. 

Having almost successfully accomplished 
the task, one of the slats will glide out from 
his structure, and the whole will be a mass 
of ruins. It was the one slat, which, owing to 
its dereliction in performing its duty, des- 
troyed the figure, and prevented all the others 
from performing theirs. 

It will not be difficult for the thinking 
teacher to derive from such an occurrence, 
the opportunity to make an application to 
other conditions in life, even within the sphere 
of the young child, and its companions in and 
out of school. The character of this occu- 
pation does not admit of its introduction be- 
fore the pupils have spent a considerable time 
in the Kinder-Garten, in which it is only be- 
gun, and continued in the primary depart- 
ment. 



THE SIXTEENTH GIFT. 



THE SLAT WITH MANY LINKS. 



This occupation material, which may be 
used at almost any grade of development in 
the Kinder Garten, the primary and higher 
school departments, is so rich in its applica- 
tions, that we cannot attempt to describe it 
extensively, nor give illustrations of the vari- 
ous ways in which it can be rendered useful. 
Suffice it to say, that it may be employed in 
representing all various kinds of lines, angles 



and mathematical figures, and that even forms 
of life and beauty may be presented by it. 

We have slats with 4, 6, 8 and 16 links, 
which are introduced one after the other when 
opportunities offer. In placing the first. into 
the hand of the child, we would ask him to 
unfold all the links of the slat, and to place 
it upon the table so as to represent a perpen- 
dicular, horizontal, and then an oblique line. 



GUIDE TO KINDER-GARTNERS. 



67 



By bending two of the links perpendicularly, 
and the two others horizontally, we form a 
right angle. Bending one of the legs of the 
angle toward, or from the other, we receive 
the acute and obtuse angles, which grow 
smaller or larger, the nearer or farther the 
legs are brought to, or from each other, until 
we reduce the angles to either a perpendicular 
line of two links' length, or a horizontal line 
of the length of four links. 

We may then form a square. Pushing two 
opposite corners of it toward each other, and 
bending the first link so as to cover with 
it the second, and, by then joining the 
end of the fourth link to where the first 
and second are united, we shall form an 
equilateral triangle. (Which other triangle 
can be formed with this slat, and how ?) 

The capital letters V, W, N, M, Z, and the 
figure 4 can be easily produced by the chil- 
dren, and many figures be constructed by the 
teacher in which the pupils may designate the 



number and kinds of angles, which they con- 
tain, as is done with the movable slats on 
other occasions. 

The slats with 6, 8 and 16 links, to be 
introduced one after the other, if used 
in the manner here indicated, can be ren- 
dered exceedingly interesting and instruct- 
ive to the pupils. Their ingenuity and in- 
ventive power will find a large field in the 
occupation with this material if, at times, 
they are allowed to produce figures them- 
selves, of which the more advanced pupils 
may make drawings and give a description 
of each orally. 

It would be needless to enlarge here upon 
the richness of material afforded by this gift, 
as half an hour's study of and practice with it 
will convince each thinking teacher fully of 
the treasure in her hand and certainly make 
her admire it on account of the simplicit)' of 
its application for educational purposes in 
school and family. 



THE SEVENTEENTH GIFT. 



MATERIAL FOR INTERTWINING. 



(PLATES LXVII., LXVIII.) 



Intertwining is an occupation similar to 
that of interlacing. Aim of both is repre- 
sentation of plane — outlines. In the occupa- 
tion with the interlacing slats we produced 
forms, which were to be destroyed again, or 
whose peculiarities, at least, had to be changed 
to produce something new ; here, we produce 
permanent results. There, the material was 
in everj' respect a ready one ; here, the pupil 
has to prepare it himself There, hard slats 
of little flexibility ; here, soft paper, easily 
changed. There, production of purely math- 
ematical forms by carefully employing a given 
material ; here, production of similar forms 



by changing the material, which forms, how- 
ever, are forms of beauty. 

The paper strips, not used when preparing 
the folding-sheets, are used as material, adapted 
for the present occupation. They are strips 
of white or colored paper, from eight to ten 
inches long and varying in breadth. Each 
strip is subdivided in smaller strips of three- 
quarters of an inch wide, which by folding 
their long sides are transformed to threefold 
strips of eight to ten inches long and one- 
quarter of an inch wide. 

The children will not succeed well, in form- 
ing regular figures from these strips at first. 



GUIDE TO KINDER-GARTNERS. 



As the main object of tliis occupation is to 
accustom the child to a clean, neat and cor- 
rect performance of his task, some of the 
tablets of Gift Seven are given him as pat- 
terns to assist liim ; or the child is led to draw 
on his slate the three, four, or many cornered 
forms, and to intertwine his paper strips ac- 
cording to these. 

First, a right angled isosceles triangle is used 
for laying around it one of these strips so as 
to enclose it entirely. We begin with the left 
cathetus, put the tablet upon the strip, folding 
it toward the right over the right angle. The 
break of the paper is well to be pressed down, 
and then the strip is again folded around the 
acute angle toward the left. Where the hy- 
potenuse (large side) touches the left cathetus 
(small side), the strip is cut and the ends of 
the figure there closed by gluing them to- 
gether by some clean adhesive matter. Care 
should be taken that the one end of each side 
be under, the other over, that of the other. 

Thus the various kinds of triangles, (Figs. 
I — 3,) squares, rhombus, rhomboids, etc., are 
produced. 

Two like figures are combined, as shown in 
Figs. 4 — 6. If strips prove to be too short, 
the child is shown how to glue them together, 
to procure material for larger and more com- 
plicated forms. Thus, it produces, with one 
long strip. Figs. i6, i8, 19, 20; with two long 
strips. Figs. 17, 21. Fig. 22 shows the natu- 
ral size ; all others are drawn on a somewhat 
reduced scale. It cannot be difficult to pro- 
duce a great variety of similar figures, if one 
will act according to the motives obtained with 
and derived from the occupation with the in- 
terlacing slats. 



This occupation admits of still another and 
very beautiful modification, by not only pinch- 
ing and pressing the strip where it forms 
angles, but by folding it to a rosette. This 
process is illustrated in Figs. 7 — 9. The strip 
is first pinched toward the right, (Fig. 7,) then 
follows the second pinch downward, (Fig. 8,) 
then a third toward the left, when the one end 
of the strip is pushed through under the other, 
(Fig- 9-) 

Here, also, simple triangles, squares, pen- 
tagons and hexagons are to be formed, then 
two like figures combined, and finally more 
complicated figures produced. (Compare ex- 
amples given in Figs. 10 — 15.) 

Whatever issues from the child's hand suffi- 
ciently neat and clean and carefully wrought, 
may be mounted on stiff paper or bristol 
board, and disposed of in many ways. 

The occupation of intertwining shows 
plainly how by combination of simple mathe- 
matical forms, forms of beauty may be pro- 
duced. These latter should predominate in 
the Kinder-Garten, and the mathematical are 
of importance as they present the elements for 
their construction. The mathematical ele- 
ment of all our occupations is in so far of 
significance, as the child receives from it 
impressions of form ; but of much more im- 
portance is the development of the child's 
taste for the beautiful, because with it, the 
idea of the good is developed in the mean- 
time. 

As the various performances of this occu- 
pation, cutting, folding and mounting, require 
a somewhat skilled hand, it is introduced 
in the upper section of the Kinder-Garten 
only. 



THE EIGHTEENTH GIFT. 



MATERIAL FOR PAPER- FOLDING. 



(plates lxix. to lxxi.) 



Froebel's sheet of paper for folding, the 
simplest and cheapest of all materials of oc- 
cupation, contains within it a great multitude 
of instructive and interesting forms. Almost 
every feature of mathematical perceptions, ob- 
tained by means of previous occupations, we 
again find in the occupation of paper-folding. 
It is indeed a compendium of elementary 
mathematics, and has, therefore, very justly 
and judiciously been recommended as a use- 
ful help in the teaching of this science in 
public schools. 

Lines, angles, figures, and forms of all 
varieties appear before us, after a few mo- 
ments' occupation with this material. The 
multitude of impressions, however, should 
not misguide us ; and we should always, and 
more particularly in this work, be careful to 
accompany the work of the children with nec- 
essarj' conversation and pleasant entertain- 
ment, for the relief of their young minds. 

We prepare the paper for folding in the fol- 
lowing manner : 

Take half a sheet of letter paper, place it 
upon the table in such a manner as to have 
the longest sides extend from left to right. 
Then halve it by covering the upper corners 
with the lower ones, (Fig. i.) Then turn the 
now left and right upper (previously lower) 
corners back, towards the center ; invert the 
paper ; turn also the two other corners toward 
the center, and then we have the form of a 
trapezium, (Fig. 2.) Unfolding the sheet at 
its base line, a hexagon, (Fig. 3,) will show 
itself; in which we obsen'e four triangles, of 



which two and two lie together, forming a 
larger triangle. At the base lines of these 
larger triangles, the sheet is again folded, and 
neatly and accurately cut, severing thereby 
the two large double, lying triangles from the 
single and oblong strips of paper. 

Each of these triangles we cut through 
from where the sides of the small triangles 
touch each other, unfold the small triangles, 
and we now have four square pieces, and one 
oblong piece of paper, (Fig. 4.) The former 
w^e employ for folding, the latter we keep for 
future use, in the occupations of intertwining, 
braiding, or weaving. 

The child should be accustomed to ±e 
strictest care and cleanliness in the cutting as 
well as the folding. 

This is necessary, because paper carelessly 
folded and cut, will not only render more 
difficult every following task, nay, make im- 
possible ever}' satisfactory result ; especially, 
should this be the case, because, we do 
not intend simply to while away our own 
and the child's precious time, but are en- 
gaged in an occupation whose final aim is 
acquisition of ability to work, and to work 
well — one of the most important claims 
hum.in society is entitled to make upon each 
individual. 

The child prepares for himself, in the man- 
ner described, a number of folding sheets, 
and submits them to a series of regular 
changes, by bending and folding, in conse- 
quence of which the fundamental forms are 
produced, from w^hich sequels of forms of 



^o 



GUIDE TO KINDER-GARTNERS. 



life and beauty are subseqently developed, 
by means of the law of opposites. 

On the road to this goal, a surprising num- 
ber of forms of knowledge present them- , 
selves. 

The sheet is now folded once more, fol- 
lowing the diagonal, (Fig. 5,) and will then 
present, when unfolded, the division of the 
square, in two right-angled isosceles triangles. 

Folded once more according to the other 
diagonal, (Fig. 6,) and again unfolded, we find 
each of the large triangles, halved by a per- 
pendicular, (Fig. 7.) Now the lower corner 
is bent upon the left, and the right one upon 
the upper, and the sheet is so folded, that it 
is divided into equal oblong halves by a 
transversal. The same is done to the op- 
posite transversal, and we have the Fig. 9, 
affording a multitude of mathematical object 
perceptions. 

If we now take the lower corner, (Fig. 9,) 
bend it exactly toward the center of the sheet 
and fold it, the pentagon, (Fig. 10,) will be the 
result. We fold the opposite corner in like 
manner and produce the hexagon, (Fig. 11,) 
and finally with the two remaining corners, 
Fig. 12" is formed containing four triangles, 
touching one another with their free sides, 
each of them again showing a line halving 
them in two equal triangles. 

If we invert 12% we have 12'', a connected 
square, in which the outlines of eight congru- 
ent triangles appear. If 12° is unfolded we 
shall see beside a multiplication of previous 
forms, parallelograms also. If we start from 
12°, fold the corners toward the middle, (Fig. 
15,) we shall receive a form consisting of 
double layers of paper, and showing four tri- 
angles, under which again, four separate 
squares are found. This is the fundamental 
form for a series of forms of life, (Fig. 16.) 

It is utterly impossible to give a minute de- 
scription how forms of life may be produced 
from this fundamental form. Practical at- 
tempts and occasional observation in the 
Kinder-Garten will be of more assistance tljan 
the most detailed illustrations and descrip- 



tions. Froebel's Manual mentions, among 
others, the following objects : A table-cloth 
with four hanging corners, a bird, a sail boat, 
a double canoe, a salt-cellar, flower, chemise, 
kite, wind-mill, table, cigar-holder, flower-pot, 
looking glass, boat with seats, etc. Still richer 
become the forms of life, if we bend the cor- 
ners of the described fundamental form, once 
more toward the middle. In connection with 
this, the manual mentions the following forms : 
the knitting-pouch, the chest of drawers, the 
boots, the hat, the cross, the pantaloons, the 
frame, the gondola, etc. For the construction 
of these forms, it is advisable to use a larger 
sheet of paper, perhaps half a sheet of letter 
paper. 

But the simple fundamental form, for the 
forms of life, is also the fundamental form for 
the forms of beauty, contained on Plate LXX., 
(Fig. 16.) Unfold the fundamental form, do 
not press the corners but first the middle of 
the upper and lower side, then the two other 
sides toward the middle of the sheet, and the 
double canoe will be the result, (hexagon with 
two long and four short sides.) If the over- 
reaching triangles are now bent back toward 
the middle. Fig. 17 appears, from which, up 
to Fig. 21, the following forms are easily con- 
structed according to the law of opposites. 

From quite a similar fundamental form, the 
series 22 — 27 originates. 

If we finally take the sheet as represented, 
in 12'' fold the lower right corner toward the 
middle, also the left upper, (Fig. 13,) also the 
two remaining corners, we shall have four 
triangles, consisting of a double layer of pa- 
per which may be lifted up from the square 
ground and which upper layer again is divi- 
ded in two triangles, (Fig. 14.) 

Invert this figure and you will have Fig. 28, 
four single squares, the fundamental form of 
a series of forms of beauty on Plate LXXI. ; 
the latter easily to be derived from this former, 
under the guidance of the well known law of 
opposites. 

The hints given in the above might be aug- 
mented to a considerable extent and still not 



GUIDE TO KINDER-GARTNERS. 



71 



exhaust the matter. They are given espe- 
cially to stimulate teacher and child to indi- 
vidual practical attempts in producing forms 
by folding. The best results of their activity 
can be improved by cutting out or coloring, 
which adds a new and interesting change to 
this occupation. A change of the fundamental 
form in three directions yields various series 
of forms of beautj', which may be multi- 
plied ad infinitum. Thereby, not only the idea 
of sequel in representations is given, but also 
the understanding unlocked for the various 
orders in nature. 

Furthermore, this occupation gives the pu- 



pil such manual dexterity as scarcely any 
other does, and prepares the way to various 
female occupations, besides being immediately 
preparatory to all plastic work. Early training 
in cleanliness and care is also one of the re- 
sults of a protracted use of the folding sheet. 
It is evident that only those children who 
have been a good while in the Kinder-Garten, 
can be employed in this department of occu- 
pation. The peculiar fitness of the folding 
sheet for mathematical instruction beyond the 
Kinder-Garten, must be apparent after we 
have shown how useful it can be made in this 
institution. 



THE NINETEENTH GIFT. 



MATERIAL FOR PEAS-WORK. 



(plates lxxii. and lxxiii.) 



We have already tried, in connection with 
the Ninth Gift, (the laying staffs,) to render 
permanent the productions of the pupils, by 
stitching or pasting them to stiff paper. We 
satisfied, by so doing, a desire of the child, 
which grows stronger, as the child grows 
older — the desire to produce by his own activ- 
ity certain lasting results. It is no longer the 
incipient instinct of activity which governs 
the child, the instinct which prompted it, ap- 
parently without aim, to destroy everything 
and to reconstruct in order to again de- 
stroy. A higher pleasure of production has 
taken its place ; not satisfied by mere doing, 
but requiring for its satisfaction also delight 
in the created object — if even unconsciously — 
the delight of progress, which manifests itself 
in the production, and which can be observed 
only in and by the permanency of the object 
which enables us to compare it with objects 
previously produced. 

To satisfy the claims of the pupil in this 



direction in a high degree, the working with 
peas is eminently fitted, although considerable 
manual skill is required for it, not to be ex- 
pected in any child before the fifth year. The 
material consists of pieces of wire of the thick- 
ness of a hair-pin, of various sizes in length, 
and pointed at the ends. They again represent 
lines. As means of combination, as embodied 
points of junction, peas are used, soaked about 
twelve hours in water and dried one hour pre- 
vious to being used. They are then just soft 
enough to allow the child to introduce the 
points of the wires into them, and also hard 
enough to afford a sufficient hold to the latter. 

The first exercise is to combine two wires, 
by means of one pea, into a straight line, an 
obtuse, right, and acute angle. What has been 
said in regard to laying of staffs in connection 
with Fig. I — 23 on Plate XXX. will sen'e 
here also. 

Of three wires, a longer line is formed ; 
angles, with one long, and one short side. 



72 



GUIDE TO KINDER- GARTNERS. 



The three wires are introduced into one pea, 
so that they meet in one point ; two parallel 
lines may be continued by a third ; finally the 
equilateral triangle is produced. 

Then follows the square, parallelogram, 
rhomboid ; diagonals may be drawn and the 
forms shown on Plate LXXIL, figures i — lo, 
be produced. The possibility of representing 
the most manifold forms of knowledge, of life 
and of beauty, is reached, and the forms pro- 
duced may be used for other purposes. The 
child may produce six triangles of equal size, 
and repeat with them all the exercises, gone 
through with the tablets, and may enlarge 
upon them. 

Or the child may prepare 4, 8, 16 right an- 
gled triangles, or obtuse angled, or acute an- 
gled triangles and lay with them the figures 
given on Plate LXXIL, etc., for the course of 
drawing, and carry them out still further. 

After these hints it seems impossible not 
to occupy the child in an interesting and in- 
structive manner. 

But the condition attached to each new Gift 
of the Kinder-Garten is some special progress 
in its course. 

We produced outlines of many objects with 
the staffs ; all formations, however, remained 
planes, whose sides were represented by staffs. 
In the working with peas, the wires represent 
edges, the peas serve as corners, and these 
skeleton bodies are so much more instructive 
as they allow the observation of the outer 
forms in their outlines, and the inner structure 
and being of the body at the same time. 

The child unites two equilateral triangles 
by three equally long wires, and forms thereby 
a prism, (Fig. 14;) four equilateral triangles, 
give the three-sided pyramid ; eight of them, 
the octahedron. (Figs. 15 and 16.) 

From two equal squares, united by four 
wires of the length of the sides, the skele- 
ton cube. Fig. 17, is formed; if the uniting 
wires are longer than the sides of the square, 
the four-sided column (Fig. 8); is one of the 
squares larger than the other, a topless pyra- 
mid will be produced, etc. 



It is hardly possible that pupils of the 
KinderGarten should make any further prog- 
ress in the formation of these mathematical 
forms of crystallization, as the representation 
of the many-sided bodies, and especially the 
development of one from another, requires 
greater care and skill than should be expected 
at such an early period of life. It will be re- 
served for the primary, and even a higher 
grade of school, to proceed farther on the 
road indicated, and in this manner prepare 
the pupil for a clear understanding of regular 
bodies. (Fig. 19 shows how the octahedron 
is contained in the cube.) 

This, however, does not exclude the con- 
struction by the more advanced pupils of the 
Kinder-Garten, of simple objects, in their 
surroundings, such as benches, (Fig. 21,) 
chairs, (Fig. 23,) baskets, etc., or to try to 
invent other objects. 

Whoever has himself tried peas-work, will 
be convinced of its utility. Great care, much 
patience, are needed to produce a somewhat 
complicated object ; but a successful structure 
repays the child for all painstaking and per- 
severance. By this exercise, the pupils im- 
prove in readiness of construction, and this 
is an important preparation for organiza- 
tion. 

More advanced pupils try also, successi.- 
fully, to construct letters and numerals, with 
the material of this Gift. 

The bodies produced by peas-work may 
be used as models in the modeling depart- 
ment. The one occupation is the comple- 
ment of the other. The skeleton cube allows 
the observation of the qualities of the solid 
cube, in greater distinctness. The image of 
the body becomes in this manner more per- 
fect and clear, and above all, the child is 
led upon the road, on which alone it is 
enabled to come into possession of a true 
knowledge and correct estimate of things; 
the road on which it learns, not only to ob- 
serve the external appearance of things, but 
in the meantime, and always, to look at their 
internal being. 



THE TWENTIETH GIFT. 



MATERIAL FOR MODELING. 

(plate lxxiv.) 



Modeling, or working in clay, held in high 
estimation by Froebel, as an essential part of 
the whole of his means of education is, strange 
to say, much neglected in the Kinder-Garten. 
As the main objection to it named is that the 
children, even with the greatest care, can not 
prevent occasionally soiling their hands and 
their clothes. Others, again, believe that an 
occupation, directly preparing for art, very 
rarely can be continued in life. They call it, 
therefore, aimless pastime without favorable 
consequences, either for internal development 
or external happiness. 

If it must be admitted that the soiling of 
the hands and clothing cannot always be 
avoided, we hold that for this very reason, 
this occupation is a capital one, for it will 
give an opportunity to accustom the children 
to care, order and cleanliness, provided the 
teacher herself takes care to develop the sense 
of the pupils, for these virtues, in connection 
with this occupation ; as on all other occasions, 
she should strive to excite the sense of clean- 
liness as well as purity. Certainly, parts of 
the adhesive clay will stick to the little fingers 
and nails of the children, and their wooden 
knives ; but, pray, what harm can grow out of 
this? The child may learn even from this 
fact. It may be remarked in connection with 
it, that the callous hand of the husbandman, 
the dirty blouse of the mechanic, only show 
the occupation, and cannot take aught from 
the inner worth of a man. As regards the ob- 
jection to this occupation as aimless and 
without result, it should be considered that 



occupation with the beautiful, even in its 
crudest beginnings, always bears good fruit, 
because it prepares the individual for a true 
appreciation and noble enjoyment of the 
same. Just in this the significance of Froebel's 
educational idea partly rests, that it strives to 
open every human heart for the beautiful 
and good — that it particularly is intended to 
elevate the social position of the laboring 
classes, by means of education, not only in 
regard to knowledge and skill, but also, in 
regard to a development of refinement and 
feeling. 

Representing, imitating, creating, or trans- 
forming in general, is the child's greatest en- 
joyment. Bread-crumbs are modeled by it 
into balls, or objects of more complicated 
form, and even when biting bits from its 
cooky, it is the child's desire to produce 
for?n. If a piece of wax, putty, or other plia- 
ble matter, falls into its hands, it is kneaded 
until it assumes a form, of which they may 
assert that it represents a baby, — the dog 
Roamer, or what not ! Wet sand, they press 
into their little cooking utensils, when playing 
"house-keeping," and pass off the forms as 
puddings, tarts, etc. ; in one word, most chil- 
dren are born sculptors. Could this fact have 
escaped Froebel's keen observation? He 
has here provided the means to satisfy this 
desire of the child, to develop also this talent, 
in its very awakening. 

According to Froebel's principle, the first 
exercises in modeling are the representation 
of the fourteen stereometric fundamental forms 



74 



GUIDE TO KINDER- GARTNERS. 



of crystallization, which he presents in a box, 
by themselves as models. Starting from the 
cube the cylinder follows — then the sphere 
pyramid with 3, 4 and 6 sides, the. prism in its 
various formations of planes, the octahcdro?t 
or decahedron and cosahedron, or bodies with 
8, 12 and 20 equal sides or faces, etc., etc. 
However interesting and instructive this course 
may be, we prefer to begin with somewhat 
simpler performances, leaving this branch of 
this department for future time. 

The child receives a small quantity of clay, 
(wa.x may also be used,) a wooden knife, a 
small board, and a piece of oiled paper, on 
which it performs the work. If clay is used, 
this material should be kept in wet rags, in 
a cool place, and the object formed of it, 
dried in the sun, or in a mildly-heated stove, 
and then coated with gum arabic, or var- 
nish, which gives them the appearance of 
crockery. 

First, the child forms a sphere, from which it 
may produce many objects. If it attaches a 
stem to it, it is a cherry ; if it adds depressions 
and elevations, which represent the dried calyx, 
it will look like an apple ; from it the pear, nut, 
potato, a head, may be molded, etc. Many 
small balls made to adhere to one another 
may produce a bunch of grapes, (Figs. 

i-S.) 

From the ball or sphere, a cylindrical body 
may be formed, by rolling on the board, usu- 
ally called by the children a loaf of bread, 
cigar, a candle, loaf of sugar, etc. 

A bottle, a bag filled with flour or some- 
thing else, can also easily be produced. 

Very soon the child will present the cube, 
an old acquaintance and playmate. From it, 
it produces a house, a bo.x, a coffee-mill and 
similar things. Soon other forms of life will 
grow into existence, as plates, dishes, animals 
and human beings, houses, churches, birds' 
nests, etc., etc. If this occupation is intended 
to be more than mere entertainment, it is 
necessary to guide the activity of the child in 
a definite direction. 

The best direction to be followed in Froe- 



bel's occupations is that for the development 
of regular forms of bodies. Fundamental 
form, of course, is the sphere. The child 
represents it easily, if perhaps not exactly 
true. 

By pressing and assisted by his knife, the 
one plane of the sphere is changed to several 
planes, corners, edges, which produces the 
cube. If the child changes its corners to 
planes (indicated in Fig. 12,) a form of four- 
teen sides is produced. If this process is 
continued so that the planes of the cube are 
changed to corners, the octahedron is the re- 
sult, (Fig. 13.) By continued change of edges 
to planes and of planes to corners, the most 
important regular forms of crystallization will 
be produced, which occupation, however, as 
mentioned before, belongs rather to a higher 
grade of school, and is therefore better 
postponed until after the Kinder-Garten 
training. 

Some regular bodies are more easily 
formed from the cylinder, the mediation be- 
tween the sphere and cube. By a pressure of 
the hand, or by means of his knife, the child 
changes the one round plane to three or four 
planes, and as many edges, producing thereby 
the prism and the four-sided column. 

If we change one of the planes of the cyl- 
inder to a corner, by forming a round plane 
from its center to the periphery of the plane, 
we produce a cone. If we change the sur- 
face of the cone to three or four planes, we 
shall have a three or four sided pyramid. If 
we act in the same manner with the other end 
of the cylinder, we shall form a double cone, 
and from it we may produce a three or four- 
sided double pyramid, etc. If we act in an 
opposite manner, destroy the edges of the 
cylinder, we shall again have the sphere. 

Well formed specimens may, to acquire 
greater durability, be treated as indicated 
previously. The production of forms and fig- 
ures from soft and pliable material belongs, 
undoubtedly, to the earliest and most natural 
occupations of the human race, and has served 
all plastic arts as a starting-point. The occu- 



GUIDE TO KINDER-GARTNERS. 



75 



pation of modeling, then, is eminently fit to 
carry into practice Froebel's idea that chil- 
dren, in their occupations, have to pass through 
all the general grades of development of hu- 
man culture in a diminished scale. The 
natural talent of the future architect or sculp- 
tor, lying dormant in the child, must needs be 
called forth and developed by this occupation, 
as by a self-acting and inventing construction 
and formation, all innate talents of the child 
are made to grow into visible reality. 

If we now cast a retrospective look upon 
the means of occupation in the Kinder- 
Garten, we find that the material progresses 
form the solid and whole, in gradual steps to 
its parts, until it arrives at the image upon 
the plane, and its conditions as to line and 
point. For the heavy material, fit only to be 
placed upon the table in unchanged form, 
(the building blocks,) a more flexible one 
is substituted in the following occupations : 
7vood is replaced hy paper. The paper plane 
of the folding occupation, is replaced by the 
paper strip of the weaving occupation, as line. 
The wooden staff, or very thin ivire, is then 
introduced for the purpose of executing per- 
manent figures in connection with peas, repre- 
senting the point. In place of this material 
the dratcn line then appears, to which colors 
are added. Perforating and embroidering 
introduces another addition to the material 
to create the images of fantasy, which, in the 
paper cutting and mounting, again receive 
new elements. 

The modeling \n clay, or wax, affords the im- 
mediate plastic artistic occupation, with the 
most pliable material for the hand of the 
child. Song introduces into the realm of 
sound, when movement plays, gymnastics, and 
dancing, help to educate the body, and insure 
a harmonious development of all its parts. 
In practicing the technical manual perform- 
ances of the mechanic, such as boring, 
piercing, cutting, measuring, uniting, forming, 
drawings painting, and modeling, a foundation 
of all future occupation of artisan and artist 



— synonymous in past centuries — is laid. For 
ornamentation especially, all elements are 
found in the occupations of the Kinder-Gar- 
ten. The forms of beauty in the paper-fold- 
ing,/. /., serve as series of rosettes and or- 
naments in relief, as architecture might em- 
ploy them, without change. The productions 
in the braiding department contain all con- 
ditions of artistic weaving, nor does the cut- 
ting of figures fail to afford richest material 
for ornamentation of various kinds. 

For every talent in man, means of develop- 
ment are provided in the Kinder-Garten ma- 
terial, opportunity for practice is constantly 
given, and each direction of the mind finds 
its starting-point in concrete things. No more 
complete satisfaction, therefore, can be given 
to the claim of modern pedagogism, that all 
ideas should be founded on previous percep- 
tion, derived from real objects, than is done in 
the genuine Kinder-Garten. 

Whosoever has acquired even a superfi- 
cial idea only of the significance of Froebel's 
means of occupation in the Kinder-Garten, 
will be ready to admit that the ordinary play- 
things of children can not, by any means, as 
regards their usefulness, be compared with 
the occupation material in the Kinder-Gar- 
ten. That the former may, in a certain de- 
gree, be made helpful in the development of 
children, is not denied ; occasional good re- 
sults with them, however, mostly always will 
be found to be owing to the child's own in- 
stinct rather than to the nature of the toy. 
Planless playing, without guidance and super- 
vision cannot prepare a child for the earnest 
sides of life as well as for the enjoyment of 
its harmless amusements and pleasures. 
Like the plant, which, in the wilderness even, 
draws from the soil its nutrition, so the child's 
mind draws from its surroundings and the 
means, placed at its command, its educational 
food. But the rose-bush, nursed and cared 
for in the garden by the skillful horticulturist 
produces flowers, far more perfect and beau- 
tiful than the wild growing sweet-briar. With- 
out care neither mind nor body of the child 



76 



GUIDE TO KINDER-GARTNERS. 



can be expected to prosper. As the latter 
can not, for a healthful development, use all 
kinds of food without careful selection, so 
the mind for its higher cultivation requires a 
still more careful choice of the means for its 
development. The child's free choice is lim- 
ited only in so far as it is necessary to limit 
the amount of occupation material in order 
to fit it for systematic application. The child 
will find instinctively all that is requisite for 
its mental growth, if the proper material only 
be presented, and a guiding mind indicate its 
most appropriate use in accordance with a 
certain law. 

Froebel's genius has admirably succeeded 
in inventing the proper material as well as in 
pointing out its most successful application to 
prepare the child for all situations in future 
life, for all branches of occupation in the 
useful pursuits of mankind. 



When the Kinder-Garten was first estab- 
lished by him, it was prohibited in its original 
form and its inventor driven from place to 
place in his fatherland on account of his lib- 
eral educational principles, to be carried out 
in the Kinder Garten. The keen eye of mo- 
narchial government officials quickly saw that 
such institution could not turn out willing 
subjects to tyrannical oppression, and the ru- 
lers "-^by the grace of God,'' tolerated the 
Kinder-Garten, only when public opinion de- 
clared too strongly in its favor. 

In pleading the cause of the Kinder-Gar- 
ten on the soil of republican America, is it 
asking too much that all may help in extend- 
ing to the future generation the benefits which 
may be derived from an institution so emi- 
nently fit to educate free citizens of a free 
country ? 



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P A- R T T . 



PARADISE OF C!HlLDHOOD 



A MAMAI. Kdli SKl.|--IXSTl!L-ClIo.\ l.V I'KIKDUICII KUOKIil- L'; 
KDrCATloNAl, I'UIXCll'I.KS. 



(jiiide to Kinder-Gartners. 



E I) W A R D W I E B E . 



WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS. 



.MILTON ]}KAULEY >!c COMPANY. 

SIMilN(il-lKLl). .MASS. 



PART IV. 



PARA DISE OF CHILDHOOD : 



A MANUAL Fol! SKLF-TN'STRUCTIOX IX FRIEnRICII FliOEBEL'S 
EDUCATIONAL PRINCIPLES, 



AND A PRACTfCAr 



(jiiide toKinder-Grartners. 



E D W A Pv D \V I E B PJ 



WITH SEVENTY- FOUR PLATES OF ILLUSTRATIONS. 



MILTON BllADLKY & COMPANY 

SPUINCI'IKLl). MASS. 



GIFTS. OR OCCUPATION MATERIAL FOR THE 

IK I H D E m«ll A»1PS». 

O0R high' estimation nl' llic tiiorits of tills system of education, lias iiuliicoil us to fit up tlic macliincr.v and 
fixtures necessary for the |ir.idiutl(in of the Occiipatiox Matkkiai. in an economical and superior manner. 

As the several (iifts have lneii prepared under the direction and liy tlie sii^'sestions of the most conipolent 
teachers of Kinder-lJartcn in tliis country, we believe they will meet with universal favor; hut any sugiiestions 
from Practical Kinder-Gartners, will be" thankfully received, and, if considered advantageous, will immediately 
be embodied in our manufactures. Price Lists furnislied to Dealers and Teachers on application. 



THE GREAT EDUCATIONAL CxAME OF 



Wi: have purchased from the Inventor the entire Patent on the above Wii\-i)i;Rrt:i, ('o.miu 
STROCTios AM) AJirsF.MF.NT, bv wliicli the jiriiiciples of 

ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION 

Are embodied in one of the most fascinating Games ever devised for Youth or Adults. There 
this will ]irove the most popular I'arlor Amu.sement even invented. Price §0.(K). 



THE NEW SCRIPTURE GAME OF 

A Combination- op 

CfniflOlli* Bible Qli®^1li#«|i 

In a very pleasine; and Instructive Game. 

-^JVIaqic ^quare^ and -^o^aic ^ablet^, 

Fon Recreation, Kntertainineiit and Instruction, presenting some curious puzzles in the iirojierties of numbers; 

adapted for use in families and school>, 

HY 

EDWARn W. OII.MAM. 

Prof. Lyman of Yale College says in a note to the author of this work : 

"Your device of 'Magic T.tblets' strikes me as one well fitted to aflbrd instruction ,and entertainment for tlie 
young, and to become popular as an evening amusement. If it shall give to the lovers of mathematical puzzles 
half Tlie gratification which I received when a boy from Magic S(|uares as commonly exhibited, the young people 
will have abundant reason tft thank you for your imjiroved method of presentation. 

" The talili'ts and book of problems are put u)) in a neat box complete." Price each, .SLOO. 

THE ZOETROPE, 

TImt OPTICAL WOXOKR— always new, with New Pictures. 

ritOF. BOVEJR'S 

LATEST MANUAL OF CROQUET, 

FOR THE FIELD OR THE PARLOR, ILLUSTRATED. 

Send 10 CEN-TS for the CnOQiin .Maxuat, and complete I'rice List of Games, etc. : or a Stamji for the Price Lists. 

MILTON BRADLKV k (()., 

Spi'iDff/ield. Mass. 



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